Most french presses are made of Pyrex, not glass, which keeps heat much better than a glass container -- if you're still worried about heat dispersion, pre-heat the press pot with hot water (205F) for a minute before you add the tea.
With regards to over-brewing tea, that's what the plunger is for. Just time your tea (3-5 minutes for green, 5-7 for black) with the plunger resting loosely on top of the tea, then plunge and serve. Your tea will keep piping hot and won't over-brew.
To answer the original question, it is not only totally acceptable but also an awesome way to drink tea! We serve all our tea in press pots along with a timer and a cup 'n saucer, and although we tend to get some funny looks it also makes for a really nice tea experience.