It may not be the heater. Healeys are famous or infamous for cockpit heat. The air comes in through the front as it should, passes through the radiator, where it gets hot from heat transfer from the radiator (as it should) then it goes on into the hot engine compartment and...does not have anywhere to go, so it tries to get through any opening or crevice there is in the firewall and transmission tunnel.
Old reviews of the Healeys said there is really no cure, but that is no longer true. A combination of insulation and a concerted effort to seal the firewall and tunnel area makes it is cool (or hot) in the cockpit as the ambient air.
I insulated my 100 and it helped a little. When I sealed it up it helped a lot. On my car most of the sealing was around the tranny tunnel and the removable piece that mates with the tunnel to become part of the firewall.