Air vents blowing hot air

This problem started about four months ago. After starting the truck, and then driving for about ten to fifteen minutes, the air vents will start blowing hot air. As if you turned the heater on, hot.
This happens whether I have the AC turned on or not.
I would be able to pull over, turn the truck off, then start it up again and the problem would be corrected.
The AC has never stopped working through this whole issue. It blows very cold.
This issue does not seem to affect any other functions, systems or negatively impact the overall operation of the vehicle when it is occurring.
I took the truck for an oil change two days ago and was told my battery failed during their testing and it needed to be replaced. So I went to the auto parts store, purchased a new battery and had them install it.
When I started the truck, I turned the fan on, but not the AC. Within less than one minute, it started blowing hot air. I turned the truck off, then started it again, and the same thing happened.
Once more, and the same result.
Now, every time I start the truck this happens. The only remedy is to turn the vents to defrost setting so bbn I do not have hot air blowing at me.
I can find nothing online about this problem. Please Help!