Some novel ideas here. First thing - the a/c or c/c must be set to on which will dry the air. Sure, crank up the heater, even open a window if you feel like it, but all that will do is vapourise the moisture, which, soon as you switch off, will condense on the coldest place, ie the windows. The only way to dry is via a/c.
The air con. will dry the air if it is functioning correctly. If not, it can cause more moisture problems than it solves. Running the system conventionally with it switched off for a good time, a whole journey through warm-up and more, will show if there is a problem there, if the condensation is less when air con. is off.
Most vehicles don't have a problem when parked as described by the OP even without aircon. If the moisture isn't in the structure of the car interior (as from sodden carpets for example), it's coming from somewhere in the heating/ventilation/air conditioning system.
If moisture is pooling in the system due to inadequate drying, blocked drains etc., then it can be carried into the car interior by evaporation through open vents due to latent warmth in the system when the vehicle is parked. It then condenses on the cold surfaces in the interior as you say.
This is why I suggested making sure all vents and inlets are closed if possible when stopping: it will illiminate the system as the source of moisture, and indicate a possible problem area.