Call me paranoid but I refuse to drink hot liquids out of plastic containers of any kind. A glass french press is the way to go.
[0] https://en.wikipedia.org/wiki/Bisphenol_A#Health_effects
[1] http://www.motherjones.com/environment/2014/03/tritan-certic...
http://www.sciencedirect.com/science/article/pii/S0016648014...
http://myplasticfreelife.com/2011/04/bpa-free-does-not-mean-...
TL;DR: Just because plastic is BPA free, doesn't mean it is safe or even better.
It doesn't mention heat, but I presume leaching increases with heat.