Dear me!
As a matter of observation (without even considering science) I have never seen condensation on the outside of a cup of hot tea but I have seen condensation on the outside of a cold glass of beer.
This would lead one to believe that condensation is not possible on the ouside of a hot heater element so if there is water in that zone the cause must be looked for elswhere; ingress of rain water, leaking washer tubes, or leaking from the engine cooling/heater system.
On the other hand all aircon systems condense water out of humid air, just like that cold beer glass, that freezing cold element is the evaporator and part of the effect is to remove humidity from the air, that is why drains for the condensed water are important.
I can assure you that after 10 years of use there is no rust on the heater control quadrant (behind the knob on the dash). If any water ever got there I would be looking for leaks higher up. The cable and the movement inside the airbox where perfectly free but the mechanism behind the dash had been assembled too tightly from new and with dried and hardened grease had become almost impossible to turn the knob.

Now to forget about aircon for a moment and discuss hot air entering the cabin; I have already mentioned the problem that the top of the airbox. From some time in the early 2000s the seal to the underside of the bonnets was changed from 2 rectangular forms, made from a rubber extrusion, either side of the bonnet hinge to an incomplete closed cell foam seal. See previous photos. Closing the gap stops hot air directly from the engine bay entering the ventilation system. None the less the design of the Morgan bonnets still means that some hot engine bay air exiting the louvres ahead of the air ventilation louvres may still enter. A better solution may be to have no top louvres on the bonnets except those dedicated to the ventilation system.

If hot air from the heater element , with the more recent trad system, is entering the cabin when not desired there are two possible reason: 1. the heater control flap is not closing completely, or 2. the hot part of the airbox, with the flap closed, is not sufiiciently insulated from the cold air chamber.
In the case of the first it may be possible that the control cable needs adjustment otherwise there must be a mechanical fault inside the box. The second issue, if there is insufficient insulation of the internals of the box (quite probable), would be much more difficult to fix. In that case Lorne's idea of a cutoff valve is quite valid however, ideally, it should be a solenoid valve linked to the dashboard heater control system. The reason for this is that a combination of hot air and air dehumidified by the aircon system is often desirable to dehumidify the inside of the car in cold rainy weather. Even with a non aircon car there would be times that you would not want to be fidling under the bonnet to get hot air.

I am somewhat inspired to experiment with a valve although I have to say that my experience is that blocking hot engine bay air from entering the top of the airbox makes a big difference.


Peter

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