I also have hypothyroidism and have wondered the same thing about increasing the dosage. There were a few times when I accidentally took a double dose (I'm at 75 mcg), but it really didn't do anything. I expected that I would have had at least a hard time sleeping or something, but nothing changed. I also have wondered about any special dietary restrictions I should do to help my condition. I would ask your endocrinologist about any diets/supplements/exercises that might help.
As far as your heart rate, do you have a hard time increasing it during your aerobic exercises? Mine seems to go up fine, but my resting heart rate can be quite low (as low as 42 bpm) and my blood pressure has been as low as 90/44. Since being on the medicine, these values have gone up a little, but I'm still cold all the time (and I live in a city where the temperatures average 110-120 in the summer!).