1999 Chrysler Town and Country Erratic Heater Temperature

My son drives a 99 Chrysler T&C. The van has full electronic hand controls (steering and throttle / brake) to allow him to drive from his wheelchair. On cold days, he uses the remote start to allow the car to warm up before he enters. Recently, the car's heater has not been blowing hot air, even when allowed to warm-up for 20 minutes. The temperature of the air from the heating vents does warm up when he is driving, but when the car's engine is still running and the car is not moving, the air temperature drops.

Though I didn't think it was the problem, I had the thermostat changed and the problem was still there. I just had the radiator flushed and it doesn't seem to have helped. If the heater core were completely plugged, I wouldn't think that the air would ever get hot, but it does when the care is moving. I have felt the inlet and outlet hoses to the heater core and the inlet is extremely hot but the outlet is not as hot (only warm). The radiator level is full and the car's tmeperature gauge is where it always has been.

Is it possible that the heater core can be partially plugged and when my some is driving, the engine RPM's causes the water pump to turn faster, creating more pressure and forcing the heated water through the partially plugged heater core? If this is the case, what would be a first step alternative to unplug the heater core rather than replacing it. The reason that I want to pursue this route first is that there is a lot of electronics and computers added to the car, to make it accessable to drive for my son, that are in the way and will have to all be removed by the installer (they are in Iowa and I live in Chicago)to get to the heater core. (In this car, is looks like they built the car around the heater core!)

Maybe it has absolutlely nothing to do with the heatwer core. In any case, appreciate any help or suggestions of things to try.