In science/thermodynamics, we use "warm up" and "cool down" to describe the *process* of adding heat or removing it from an object, i.e. it's being *acted* on, so we do say things like: "There was a rapid cool down when the electronics box was turned off." or "The hardware cooled down after we turned off the electronics box." In the phrase where you mention a heater, we wouldn't say "Cool down the heater", we would say "turn down the thermostat" or "turn down the heater".

The verb is used for people cool down = to become less hot over time e.g. I have walked in the sun for a long time and now need to cool down by having a cold shower. It can be used if someone is angry cool down = become less angry over time e.g. You get angry easily and say hurtful things. If someone annoys you, just cool down and then speak later.