BrewPi controls the fridge setting to adjust the beer temperature. The fridge setting is the beer setting plus a PID part.
From the web interface, you can see how the current fridge setting has been calculated. This makes it a lot easier to tweak the algorithm to work well for your fridge.
To control the fridge temperature, BrewPi uses a predictive on-off algorithm: it turns off the cooler when it expects that the overshoot will land exactly on the target temperature. The estimators to predict this overshoot are self-learning.
You can see how it performs here.