[ShadowAce]

Compressor puts out heat from its exhaust, while it cool the air in the fridge. They'll either cancel each other out or it'll get warmer.

By "thermostat" I meant household thermostat, controlling A/C or heat.

[Freelance Warrior]

Compressor puts out heat from its exhaust, while it cool the air in the fridge. They'll either cancel each other out or it'll get warmer

It gets warmer, reason: the fridge works by putting heat out from the inside compartment and dissipating it outside. When the door is open the two processes cancel each other, but since the equipment (electrical motor and etc) isn't perfect some electrical energy doesn't do useful work and is dissipated outside as heat. This causes the room to warm up. The fridge's thermostat won't stop the process since the desired temperature is never reached. You don't need any extra information for this problem.

[Freelance Warrior]

Compressor puts out heat from its exhaust

The household fridge's compressor is typically powered by an electrical motor, no exhaust. Furthemore, the freezing fluid pipework is sealed, no exhaust here.