We have a pilot chilling plant in which we need a much finer control over the cooling cycles.

Many, many moons ago I made laboratory constant temperature boxes by refurbishing refrigerators. We found that the only way to keep the temp constant was a combination of the compressor and a heater (a 60W light bulb) where the heater compensated for the coolers overshoot.

just an old experience, maybe you can use it.

Erik