1. A PID controller wouldn't be necessary for a brew fridge.
2. It wouldn't work because there's only one circuit so you wouldn't be able to turn the fridge on when too warm, the heater when too cool, it would be one or the other.
If you want to self-build you need one of these
In addition you need wiring and connectors, a box to install it, a plug, two sockets - one for the fridge, one for the heater.
You might find it easier to get one of these, unless you want to use a brewpi or something