Flyman,
This is an interesting problem. Our A320 FCOM procedure for AIR PACK 2 REGUL FAULT makes no mention of turning the HOT AIR off, though with loss of the Hot Air Regulating Valve, the Trim Air Valves are automatically closed. Depending on whether it is the pack Primary Channel, or the Primary AND Secondary channels of the Pack regulator which have failed, it does mention that the pack is at a fixed temperature. Mention is also made of the pack air inlet and outlet valves opening fully OR, the pack outlet temperature is regulated by the anti ice valve to a temperature of between 5 and 30 degrees C.
As Pack 2 serves the FWD and AFT cabin in the situation of loss of Hot Air Regulation according to the FCOM, whichever of the situations above it is, and all other parts of the air conditioning system being serviceable, you could assume that the lower than desired cabin temperatures are as a result of the fixed pack temperature from Pack 2. So, just by turning off Pack 2, you should still have a fully functioning and regulating temperature source from Pack 1 anyhow which will then serve the whole aircraft.