You should drink as many as you like, but if you're using a teabag, remove it once the tea is done steeping. Peegies turned me onto this trick; not only does the tea taste better when you make it weaker, but you can use the teabag again for 2x tea power. If you use loose leaf, you're out of luck, I suppose.
I tried a jasmine tea today that was amazing. It was like drinking daffodils! (the brand is yamamotoyama if anyone wants to try it)
Anyway, sounds like what you need is a better insulator. I typically drink out of styrofoam cups at the office, and if I put my cup inside another cup, it stays hot forever, nearly. To reduce heat transfer you'll want some material that is a good insulator (e.g. not metals. Something with either vacuum or air-space between two layers is the best)