I don't get why you guys are trying to eliminate the heater core? It barely weighs anything at all, I'd much rather deal with the extra few pounds (if that) than freeze my ass off and get sick, or not be able to see through the window and crash and potentially hurt/kill myself.
The heater core weighs what, like a few pounds? Then you want to throw in a 12V heater? That heater probably weighs the same if not more.
Before you start arguing with me that it's a race car, and real race cars don't have heater, Take a look at this picture, specifically in the red circle:
That's the interior of the Audi R18 etron which won Le Mans. If having a heater in the car is good enough for Le Mans and Audi's racing program it's good enough for me.