have you checked the actual temperature of the coolant when the engine has been run? if the air is coming out of the vents too cool, and the radiator is HOT then there is a core problem, but… if the radiator is cool as well, then the thermostat may be broken.
the diverter valve mentioned by TT is suspect if the temp is ok for a while, then if you change the temp selection and it goes haywire. have you had a temp problem in the summer with the AC? like, if you had the ac on, and change the temp the ac won’t cool? there is no diverter valve on this truck.
you mention flushing the heater core. if you have been able to flush it, then it isn’t clogged!!!
how did you flush it? by removing the hoses inside the engine comp at the fire wall?. my money is on the thermostat or the water pump is failing.
how long has the is been happening? what year truck?