Heat is the measure of how fast a particle is moving. "heating" means transmitting energy into particles so that they move faster.
So in your scenario the laws of physics change so that there is some kind of force that can slow particles down or suck energy out of them. In such a scenario absolute 0 would quickly be reached. Absolute 0 has specific properties such as unlimited amount of computations per joule being possible due to basically no waste heat being transmitted.
If there was such a force we would solve entropy.
