That is incorrect. Garam does indeed mean hot, but individual spices in garama masala don't need to be roasted, in fact I believe most, if not all, of them are not roasted, rather simply ground together.
The garam refers to the taseer (in Ayurvedic terms) of the spice blend, as in is it cooling (such as fennel is cooling), or is it warm (such as black pepper is warm/hot) to the body.
Almost all, if not all, of the ingredients of garam masala are warming to the body.