What you are describing is called "system identification". If you have a simple mathematical model, it is possible (and in the case of your fermentation chamber, it should be) to measure a couple of step responses and estimate the parameters to design a control system.

Finding good Kp, Ki, Kd gains by just sampling the [Kp, Ki, Kd]- space at random and trying it out on the real system is often not recommended. Firstly, because the state space is relatively large. Secondly, many systems can fail catastrophically if they become unstable, causing potential harm to man and machine. The second objection does not apply to a wine fermentation chamber, as far as I can see.