There is still a heater core, there is also still an evaportor, they are co located at the back of the dash against the firewall. The heater is still nothing more than a radiator full of hot water with air blowing across it, the evaportaor is behind it and the same blower blows air across it to cool the air. It is old school yes, but not much has changed really. If your car is running hot you still can turn on the heater and open the heater core to help cool it down. When the AC is on the heater core should be closed off. If it is full of hot water exactly what he described would happen, it is pretty simple really. The part is called an:
Actuator , Mode valve
AIR CONDITIONER & HEATER » Upper case
Pontiac › Solstice › 2006-2009
List Price : $ 37.17
Your Price :$ 29.74
I am sure is is a biatch to get to but sounds like it is not working. I am just trying to figure out why when he changed the battery it quit working. Sounds like something got unplugged or a fuse blew if it is an electric controlled valve.