Have no a/c or heater just blows ambient air - 1996 Ford Explorer

most likely that the climate control is doing the job that it is set on
the system works by running the ac and the heater together to maintain a set cabin temp
The ambient temp sensor is part of the air intake monitoring system that reports to the ECM so that the correct air/fuel ratio can be obtained for starting and running in all temperatures

The air from the heater core will be as hot as the coolant temperature of the engine. 80 Degrees is the opening temperature of the thermostat and that will be where it remains until the engine starts to work or the ambient temperature rises.
Thermostats come in a couple of different opening temperatures so check around for one that opens around 85 degrees if you want hotter air in the cab
Another point is to close the recirculating vent door to the cabin as the heater core is trying to heat fresh freezing air if it is open

Chances are it is indeed the heater core as even a spent heater unit will blow hot air off the engine when the ambient temps are hot . When the temps drop, the heat from the engine block is not enough to heat the cab properly. Have you tried the old cardboard in front of the radiator trick? Speaking of semi's,ever notice they cover their radiators in the winter? That's because it helps get their block temps up a little higher and assists with heating as well. It's not much help but do the buyer a favour and let them know beforehand. Have a good one. :)

check the heater inside under the dash and make sure the actuator motor is opening and closing the doors fully on the heater to direct the heat and ac.

It sounds like your blend door isn’t operating correctly . The blend door simply is a flap that is designed to close off heater core when it’s calling for A/C , and opposite for heat . Check to see if it’s operating

possible heater hot water control valve. if equipped would be found on one of the heater hoses under the hood. also try cafeully pinching the heater hoses to stop water flow.

make sure the compresser is turning on and off
if not there might be a leak that was missed

heater core may need to be flushed

Does the car run cold or is the temp. correct. Check the thermostat first. check that the radiator and res. is full. Check the hoses to and from the heater core. If one is hot and one is cold then either the shut-off valve to the heater core is defective or the heater core is plugged.

I would suggest changing the control head. You should be able to source a used unit from a local salvage yard.