Once it reaches your desired temp, the compressor will run less often and cool off...Its just that first run out of the gate thats stressfull.. Just keep the doors closed, keep the fan running and ya should be fine..
I use a freezer with a johnson controller on mine, and the compressor runs maybe once every 4 hours..but when I put a new keg into my kegerator that bitc%^ runs every 30 min, and yes it heats up buts once it hits it desired temp she cools off and runs less often. Hopefully this gives ya some piece of mind.