I've heard something about this before - probably on some documentarry or something. My understanding was that Neanderthals didn't cope as well as humans in the heat, allowing us an advantage, so we out-compeated them for food, driving them into smaller and smaller areas, then even in cold climates, we still kicked their arse with our funcky threads (thus evening up the advantage they had), and eventually there wasn't enough of them to be a sustainable species and they died out.
You know all those pictures of Adam and Eve where they have belly button? Think about it..................... take as long as you need........................