Some Cushing's dogs may also be affected with Hypothyroidism so testing for hypothyroidism is often part of the diagnostic process we go through with our Cushing's dogs. A full thyroid panel can be run from a single blood sample. Two of the tests that are usually included in a thyroid panel to check thyroid function are Canine TSH and Free T4 by equilibrium dialysis

Here is an excellent website about Canine Hypothyroidism which may affect our pets:

Sometimes a Cushing's dog may be truly hypothyroid and need to be taking medication for that condition along with the Cushing's medication they are prescribed. But there is also a form of hypothyroidism called "Sick Euthyroid Syndrome" or "non-thyroidal illness" which may actually only be secondary to (caused by) another condition such as Cushings, and this type of hypothyroid condition will often resolve without need for medication once the excessively high cortisol production caused by the Cushing's is lowered and brought under good control.

from the above website:

The first scenario is called the sick thyroid syndrome or nonthyroidal illness (NTI).

In this situation the thyroid gland is normal, but there are factors that are suppressing it from secreting a normal amount of thyroxine into the bloodstream. These factors include medications like cortisone, valium, anticonvulsants, and sulfa antimicrobials. Diseases like Cushing's disease, diabetes mellitus, chronic renal failure, liver disease, and Addison's disease can also cause NTI.

When these factors are corrected, or these diseases are treated, the apparent hypothyroid problem corrects itself. No treatment with supplemental thyroxine is needed.

In the second scenario the thyroid gland is having a problem secreting adequate thyroxine due to one of the causes previously mentioned in the causes section. This is the hypothyroidism we need to treat with supplemental thyroxine.

How do we differentiate between a true hypothyroidism from the sick thyroid syndrome?

We have another blood sample that aids us, called the free T4 test by equilibrium dialysis. If this is low, and the signalment, history, and physical exam are consistent with this disease, then a diagnosis of hypothyroidism is made.
A knowledgeable Vet should know how to tell the difference between true Hypothyroid condition that requires medication and a case where the dog only has a "Sick Euthyroid" or "non-thyroidal illness" which does not require medication.

Here is another good website about thyroid function:

and here's a link to another page on that website about Hypothyroidism which has some really good photos (if you put your mouse arrow over any of the photos and hold the mouse arrow there the picture will stop moving and stay still to give a better view)

Some of the symptoms of Hypothyroidism are very similar to some of the symptoms of Cushing's, so it can get confusing ...

A knowledgeable Vet should be able to figure out if the dog has Cushing's and is also truly Hypothyroid (and therefore needs medications to treat both conditions) or if the pet has Cushing's and "Sick Euthyroid Syndrome" (which would resolve once the cortisol levels are well controlled and without needing specific thyroid meds), or if the pet has only Cushing's or only a True Hypothyroid Condition, each of which would have a separate treatment protocol.