Check with your doctor, but typically we are told to limit exercise while we are still hyperthyroid. There are a few reasons ~ first, our muscle "tear down" mechanism is accelerated, while our muscle "rebuild" mechanism is suppressed, so you can actually lose more muscle mass if you exercise than if you don’t. Muscle mass is very important ~ it burns calories even at rest ~ so you don’t want to lose it if you can help it. Most of the weight loss people have when they are hyper is muscle mass, so it is NOT the good type of weight loss.
In addition, hyperthyroidism can cause irregular heartbeats, which can be very dangerous because they can get out of control. Obviously, exercise speeds up the heart rate, which may complicate matters further.
I’d stay off your cycle until you talk with your doctor.