Hi Fishous

THe biggest problem with hyperthyroidism and exercise is an 'impaired' cardiovascular and respiratory response to exercise, and so people with hyperthyroidism have low exercise tolerance. For example, there is a decrease in ventilation, tidal volume, and increases in oxygen consumption, which basically means that patients cannot increase their breathing by as much as a normal individual, and the result is difficulty exercising. SO the programme must take this into account. There are no huge dangers involved - it's not as though the inability to increase ventilation is going to cause harm, because the body would force you to stop before this happened, but the key is that the intensity of the training must be monitored to ensure that the patient can actually do the session.
But there is really nothing special that you have to avoid - it's the same programme but at reduced intensity and also making smaller increases, just to make sure the person is adapting to the training as they should.

The other practical issue, I guess, is weight loss, because as you will no doubt know, one of the symptoms of hyperthyroidism is weight loss and adding exercise increases the metabolic/energy demand and so the diet must be matched to both the lifestyle and the disease.

Good luck