Volvo P1800 heat build-up in passenger compartment

My newly-purchased 1965 P1800 produces excessive heat in the passenger compartment. The heat switch is in the “off” position. I’m not sure whether this is coming from under the hood or from the exhaust system. Engine and oil temperatures are appropriate. Might this be a heat shielding problem? Other suggestions?

Are you sure heat is not coming from the heater core, even though the heat switch is “off?”

If it’s not that, then it’s coming from the engine, transmission, and/or the exhaust system. Pull the carpet back and feel the fire wall and the floor until you figure out where the heat is coming from. Then install shielding and/or insulation.

Thanks for the advice, mcparadise. My dealer needed to adjust the heater valve (your suggestion 1) and plug some holes in the firewall (suggestion 2). I’ve also begun laying down Dynamat Extreme along the firewall and floor to increase the insulation.