Could you give a short description of what this vacuum heater valve looks like? I also don't see how pushing the gas pedal would affect the heating. These are probably two different problems.
I'm not that car fluent, but am I right in the assumption that when the heater valve opens, heat is dissipated into the cabin and when it's closed heat is held in place? So it could be that it's stuck in the open position because it's broken or because this vacuum check valve isn't providing adequate suction. Then is there any way I could manually close this heater valve?