The heater blowing cold is because of low coolant level in your radiator, either because of overheating and pushing the water out. or because of a leak and low coolant can cause overheating,
Plugger radiator fins would cause overheating on the highway, not when you slow down.
The first thing to do is to fill your radiator with the engine cold. You can use water if you are in no danger of freezing (just until you have this problem solved. Do this several times with the engine cold each time).
If you car stops overheating, then cet the cooling system pressure tested to find the leak.
If it still overheats, see if your radiator fan is running with the engine hot and the A/C and defroster off.
If the fan isn't running with the engine overheating- thats is your problem and you have a bad fan relay, fan motor, or fan controller.
If you fan is running, your radiator is full , and it still overheats only at slow speeds I am stumped.
I didn't mention a head gasket because I have never seen one overheat at low speed and not on the highway.
The only overheating problem I have seen that was really hard to diagnose was on a car that someone had repaired the fan wires and hooked them up backwards- it would only overheat at 45-50 mph.i