More then likely you have a restriction in the heater core or are low on coolant. When you accelerate you are pushing more coolant through the system.
If it were me, I would pressure test the cooling system after you make sure it is full. Make sure there are not leaks and then I would replace the heater core.
Normally we would need to do a little more testing before we do this just to confirm it because it is a pretty large job. However, it is pretty clear that would be the issue and on your vehicle it is not difficult. I attached the procedure.
If you would like to confirm it, use a laser temp gauge on the heater hoses going into the heater core. Clearly they should be about the same. If not then you have a restriction in the heater core.
Images (Click to enlarge)
Friday, October 30th, 2020 AT 1:58 PM