Uh. That's VERY weird... Does it overheat still when you turn on a/c? When turning on a heater, the car heater will actually make the car even more hotter...
Goto a Honda dealer.
In my opinion, Suzuki is plainly disgusting. I'd suggest getting a different car. All the used Suzuki cars make noise and if not, the company probably put some magical potion in it to prevent sounds. Bound to make sounds somehow.
Wouldn't give it a look.