Control system for a temperature controller

I have adapted a refrigerator to create a temperature controlled environment for brewing beer. I have mounted an electric heater coil inside the fridge and configured a basic controller to maintain a constant temperature inside the fridge. When the temperature at the temperature probe, $$T_p$$, is below the target temperature, $$T$$, the heater is turned on. When $$T_p$$ is above $$T$$, the fridge compressor is turned on. The target temperature, $$T$$, is in fact a small range to stabilise the system.

$$T_p \lt T-c \ \ \rightarrow \ \ Heat$$ $$T_p \gt T+c \ \ \rightarrow \ \ Cool$$

My question is this: I am trying to decide, more for interest than anything else, whether it is more effective to probe the temperature of the air inside the fridge, or the liquid (beer) inside the plastic vessel inside the fridge?

My instinct says that I should probe the air temperature, because the temperature of the beer will follow the temperature of the air, subject to a time delay, and by probing the temperature of the beer I could get unstable feedback due to this delay? Would the answer change if I were to put the fridge outside, where the air temperature is subject to much more variation? I suspect in this case it might be better to probe the beer so that the controller can over-compensate with air temperature and limit temperature variation of the beer.

For the purposes of this application, the control system is fixed as I'm using a fixed controller ie. heating and cooling are binary on/off functions. However I'd be interested to learn of any control techniques that could be implemented with a raspberry pi, if they were suggested!