The air con itself cools the air.
The 156 heater unit works with water circulating through it all the time, but then varies the amount of air that goes through the heater matrix.
First thing to check is that the engine is getting up to temperature. If not then the thermostat is probably shot. However I would be surprised if even with the thermostat stuck wide open you got no heat.
Next thing is that to get heat the 156 has a flap in the heater that adjusts whether air goes through the heater matrix. This flap is controlled by a servo and these can fail (mine failed last Christmas). You can change them yourself. There are 2 of them in the drivers (rhd) footwell, one of which is for the temperature adjustment and they are a bit of a pain as you land up having to change them while lying upside down with your head in the drivers footwell.
All the best