The best methods of stimulating thyroid output, and thus increase metabolism, are exercising and (over)eating. Sleep also plays a large role in thyroid (and all hormone) regulation. Provided you are getting proper sleep, I suggest eating more and working out more. In order to eat more and not gain weight you need to expend more energy.
Think of it this way: if you eat more and exercise more and have the same net energy loss you will improve your body composition much better than eating less and exercising less. There is something called G-Flux that was coined by one of the authors here regarding this idea, or something similar.
eat less, work less
eat 2000 calores + 1500 calories of work = 500 cal deficit
eat more, work more
eat 2500 calories + 2000 calories of work = 500 cal deficit
This second option will help restore your thyroid function while still resulting in weight loss, and subsequently is better for both performance and body composition. If you aren't already doing so, I suggest eating more frequently, spreading your total food intake over five to seven meals per day instead of just two or three.
Even though you are eating the same amount of food, the meal timing is beneficial for both thyroid activity (metabolism) and body composition.
These are the basics of thyroid function and exercise/diet. Let us know if you have any additional questions.