Hot air blows when motor is under strain

It might be a vacuum actuator on your model, I'd have to look that up, but this type of problem was common back in the era of vacuum actuators. You put the engine under heavier load, and it can't produce enough vacuum, so some actuators move - in your case, the temperature blend door is opening to the heater core. Then when you let off, it moves back. A bigger vacuum reservoir can help, you can also get some aftermarket setups that run off the battery.

I suspect a leaking vacuum hose. Check the hose that goes to the vacuum tank. My F150 did the same thing and it was just a hose that had rotted off.

FoR, that's probably just it, a leaky vacuum line. When engine vacuum drops, combined with loss of vacuum from leak, the actuator moves. Thanks for clarifying.