You may find the following article helpful (which really applies to any
pet, not just dogs):

How Do You Know When It's Time?
by Hilary Brown

I don't subscribe to the idea that dogs "will let us know when it's
time", at least not in any conscious sense on their part.   For one
thing, I've found in my years of counseling folks who have ill pets and
often accompanying them through the euthanasia process, that this notion
is often interpreted in a way that puts a lot of pressure on people when
they're already stressed and grief-stricken.  "What if I miss the
signs? He looked miserable yesterday but not today.  What if I act too
soon or not soon enough?  How could he ever let on that he wants it to
end?  But maybe I'm deluding myself that he feels better than he
does."
Dogs are not people.  We lovingly anthropomorphize our dogs during our
time together and there's no harm in that, even quite a bit of reward
for both them and us.  But the bottom line is that they are not people
and they don't think in the way people think.  (Many of us would argue
that that speaks to the superiority of dogs.) These amazing beings love
us and trust us implicitly.  It just isn't part of their awareness
that they should need to telegraph anything to us in order for their
needs to be met or their well-being ensured. They are quite sure that
we, as their pack leaders, operate only in their best interest at all
times.  Emotional selfishness is not a concept in dogdom and they
don't know how hard we sometimes have to fight against it ourselves.
Dogs also have no mindset for emotional surrender or giving up.  They
have no awareness of the inevitability of death as we do and they have
no fear of it.  It is fear that so often influences and aggravates our
perceptions when we are sick or dying and it becomes impossible to
separate the fear out from the actual illness after a while.   But
that's not the case with dogs.  Whatever we observe to be wrong with
our sick dogs, it's all illness.  And we don't even see the full
impact of that until it's at a very advanced point, because it's a dog's
nature to endure and to sustain the norm at all costs.  If that
includes pain, then that's the way it is.  Unlike us, they have never
learned that letting pain show, or reporting on it, may generate relief
or aid.  So they endure, assuming in their deepest doggy subconscious
that whatever we abide for them is what is to be abided.
If there is a "look in the eye", or an indication of giving up, that we
think we see from our beloved dogs, it isn't a conscious attitude on
their part or a decision to communicate something to us.  It's just an
indication of how tired and depleted they are.  But they don't know
there's any option other than struggling on, so that's what they do. 
We must assume that the discomfort we see is much less than the
discomfort they really feel.  And we do know of other options and it
is entirely our obligation to always offer them the best option for that
moment, be it further intervention, or none, or the gift of rest.
From the moment we embrace these animals when they first grace our
lives, every day is one day closer to the day they must abandon their
very temporary and faulty bodies and return to the state of total
perfection and rapture they have always deserved.  We march along one
day at a time, watching and weighing and continuing to embrace and
respect each stage as it comes.  Today is a good day.  Perhaps
tomorrow will be, too, and perhaps next week and the weeks or months
after.  But there will eventually be a winding down.  And we must
not let that part of the cycle become our enemy.
When I am faced with the ultimate decision about how I can best serve
the animal I love so much, I try to set aside all the complications and
rationales of what I may or may not understand medically and I try to
clear my mind of any of the confusions and ups and downs that are so
much a part of caring for a terminally ill pet.  This is hard to do,
because for months and often years we have been in this mode of weighing
hard data, labs, food, how many ounces did he drink, should he have his
rabies shot or not, etc.   But at some point it's time to put all of
that in the academic folder and open the spiritual folder instead.  At
that point we are wise to ask ourselves the question:  "Does he want
to be here today, to experience this day in this way, as much as I want
him to?"  
Remember, dogs are not afraid, they are not carrying anxiety and fear of
the unknown.  So for them it's only about whether this day holds
enough companionship and ease and routine so that they would choose to
have those things more than anything else and that they are able to
focus on those things beyond any discomfort or pain or frustration they
may feel. How great is his burden of illness this day, and does he
want/need to live through this day with this burden of illness as much
as I want/need him to?  If I honestly believe that his condition is
such, his pleasures sufficient, that he would choose to persevere, then
that's the answer and we press on.
If, on the other hand, I can look honestly and bravely at the situation
and admit that he, with none of the fear or sadness that cripples me,
would choose instead to rest, then my obligation is clear.  Because he
needs to know in his giant heart, beyond any doubt, that I will have the
courage to make the hard decisions on his behalf, that I will always put
his peace before my own, and that I am able to love him as unselfishly
as he has loved me.
After many years, and so very many loved ones now living on joyously in
their forever home in my heart, this is the view I take.  As my
veterinarian, who is a good and loving friend, injects my precious one
with that freedom elixir, I always place my hand on top of his hand that
holds the syringe.  He has chosen a life of healing animals and I know
how terribly hard it is for him to give up on one.  So I want to
shoulder that burden with him so he's not alone.  The law of my state
says the veterinarian is the one licensed to administer the shot, not
me.  But a much higher law says this is my ultimate gift to my dog and
the responsibility that I undertook on the day I welcomed that dog into
my life forever.

Megan

                                   

You may find the following article helpful (which really applies to any
pet, not just dogs):

How Do You Know When It's Time?
by Hilary Brown

I don't subscribe to the idea that dogs "will let us know when it's
time", at least not in any conscious sense on their part.   For one
thing, I've found in my years of counseling folks who have ill pets and
often accompanying them through the euthanasia process, that this notion
is often interpreted in a way that puts a lot of pressure on people when
they're already stressed and grief-stricken.  "What if I miss the
signs? He looked miserable yesterday but not today.  What if I act too
soon or not soon enough?  How could he ever let on that he wants it to
end?  But maybe I'm deluding myself that he feels better than he
does."
Dogs are not people.  We lovingly anthropomorphize our dogs during our
time together and there's no harm in that, even quite a bit of reward
for both them and us.  But the bottom line is that they are not people
and they don't think in the way people think.  (Many of us would argue
that that speaks to the superiority of dogs.) These amazing beings love
us and trust us implicitly.  It just isn't part of their awareness
that they should need to telegraph anything to us in order for their
needs to be met or their well-being ensured. They are quite sure that
we, as their pack leaders, operate only in their best interest at all
times.  Emotional selfishness is not a concept in dogdom and they
don't know how hard we sometimes have to fight against it ourselves.
Dogs also have no mindset for emotional surrender or giving up.  They
have no awareness of the inevitability of death as we do and they have
no fear of it.  It is fear that so often influences and aggravates our
perceptions when we are sick or dying and it becomes impossible to
separate the fear out from the actual illness after a while.   But
that's not the case with dogs.  Whatever we observe to be wrong with
our sick dogs, it's all illness.  And we don't even see the full
impact of that until it's at a very advanced point, because it's a dog's
nature to endure and to sustain the norm at all costs.  If that
includes pain, then that's the way it is.  Unlike us, they have never
learned that letting pain show, or reporting on it, may generate relief
or aid.  So they endure, assuming in their deepest doggy subconscious
that whatever we abide for them is what is to be abided.
If there is a "look in the eye", or an indication of giving up, that we
think we see from our beloved dogs, it isn't a conscious attitude on
their part or a decision to communicate something to us.  It's just an
indication of how tired and depleted they are.  But they don't know
there's any option other than struggling on, so that's what they do. 
We must assume that the discomfort we see is much less than the
discomfort they really feel.  And we do know of other options and it
is entirely our obligation to always offer them the best option for that
moment, be it further intervention, or none, or the gift of rest.
From the moment we embrace these animals when they first grace our
lives, every day is one day closer to the day they must abandon their
very temporary and faulty bodies and return to the state of total
perfection and rapture they have always deserved.  We march along one
day at a time, watching and weighing and continuing to embrace and
respect each stage as it comes.  Today is a good day.  Perhaps
tomorrow will be, too, and perhaps next week and the weeks or months
after.  But there will eventually be a winding down.  And we must
not let that part of the cycle become our enemy.
When I am faced with the ultimate decision about how I can best serve
the animal I love so much, I try to set aside all the complications and
rationales of what I may or may not understand medically and I try to
clear my mind of any of the confusions and ups and downs that are so
much a part of caring for a terminally ill pet.  This is hard to do,
because for months and often years we have been in this mode of weighing
hard data, labs, food, how many ounces did he drink, should he have his
rabies shot or not, etc.   But at some point it's time to put all of
that in the academic folder and open the spiritual folder instead.  At
that point we are wise to ask ourselves the question:  "Does he want
to be here today, to experience this day in this way, as much as I want
him to?"  
Remember, dogs are not afraid, they are not carrying anxiety and fear of
the unknown.  So for them it's only about whether this day holds
enough companionship and ease and routine so that they would choose to
have those things more than anything else and that they are able to
focus on those things beyond any discomfort or pain or frustration they
may feel. How great is his burden of illness this day, and does he
want/need to live through this day with this burden of illness as much
as I want/need him to?  If I honestly believe that his condition is
such, his pleasures sufficient, that he would choose to persevere, then
that's the answer and we press on.
If, on the other hand, I can look honestly and bravely at the situation
and admit that he, with none of the fear or sadness that cripples me,
would choose instead to rest, then my obligation is clear.  Because he
needs to know in his giant heart, beyond any doubt, that I will have the
courage to make the hard decisions on his behalf, that I will always put
his peace before my own, and that I am able to love him as unselfishly
as he has loved me.
After many years, and so very many loved ones now living on joyously in
their forever home in my heart, this is the view I take.  As my
veterinarian, who is a good and loving friend, injects my precious one
with that freedom elixir, I always place my hand on top of his hand that
holds the syringe.  He has chosen a life of healing animals and I know
how terribly hard it is for him to give up on one.  So I want to
shoulder that burden with him so he's not alone.  The law of my state
says the veterinarian is the one licensed to administer the shot, not
me.  But a much higher law says this is my ultimate gift to my dog and
the responsibility that I undertook on the day I welcomed that dog into
my life forever.

Megan

                                   

In humans, there are treatments for hyperthyroidism.  There is medication
for mild cases.  In severe cases, they remove the thyroid glands and have
the person take replacement hormone for the rest of his life.  I don't know
if they make replacement hormone for cats.  Giving a cat something every day
could be difficult.