Headgasket failure is rare but not unheard of on the V6's.
HBV is the Heater Bypass Valve which controls the flow of hot water into/out of the heater matrix (small radiator) in the car. It is operated by vacuum through narrow bore plastic pipes. They regularly fail, one way or another.
The thermostat is the device which initially restricts the flow of water through the main vehicle radiator in order to get the engine up to running temperature quickly and, thereafter, varies the flow through the rad so as to help keep the engine at its optimum running temp, assisted by the cooling fans as and when required.
Climate control is reset by holding the auto and off buttons in for several seconds with ignition on. You will hear the varuious servos etc resetting (hopefully) and if it works, is a cheap quick fix.