A well designed cheese vat wouldn't have that problem. As I've discussed elsewhere, there's no reason to have an overshoot in a cheese vat. Typically the overshoot in a feedback control for a mechanical system is a result of momentum, but there's no momentum in thermal systems. What happens in cheese vats is too much energy is produced in whatever is surrounding the milk and then the temperature goes too high. If the P is turned down, the D is turned off, and the I is adjusted correctly, you can have a response that doesn't get to the set temperature quite as fast, but doesn't overshoot at all. Most of us aren't patient enough to make that happen, and instead tolerate a 1 degree overshoot (since, who trusts that their thermocouple/thermistor is actually that precise, anyway?). I suppose I wonder what other systems (besides a PID) people use that reach the set temperature as fast and have as little overshoot. Manual control of the temperature means slow rise time or overshoot, as well (unless you just pull your pot of milk from the hot water bath the second it reaches temperature).