Hi,
I don't know of any specific heart tests that are used for this purpose. In hyperthyroidism, the general rule is that you can exercise at a level you're accustomed to when your thyroid hormone levels, FT4 and FT3, are in the normal range.
You wouldn't want to suddenly start a new strenuous program but if you're conditioned and have been doing these exercises before your diagnosis it should be ok to continue them. If your thyroid hormone levels are still high and your heart rate is elevated at rest, then you'd need to only perform light exercise. Best, Elaine