93 190e AC is Cold, then blows hot, Heat blows hot, then cold

Can you help?
When I run the AC, it blows cold for about 10 minutes, then starts
blowing hot and humid air. Turn the car off, and it runs fine, again
for about 10 minutes.
The heater does the same thing, in reverse. Just when the car gets warm
enough, it starts blowing cold air. Turn the car off, it runs fine,
again for about 10 minutes.

My 190e's been in the shop several times for this problem. Last time,
the mechanic told me I needed a new ac compressor, etc. I don't see
that fixing the heater problem.

It would seem to me that it's like a "Thermostat (like central air/heat
in your home)" issue. Like when it gets to a certain temp inside the
car, it cuts off and doesn't realise it's fallen away (either up/down)
from the desired temp and can't recover until the car is turned off and
on again. (Grasping at straws here).

Thanks in advance.