A nuc sized box works good for a queen cell incubator. You want to make it deeper if you are using a light bulb as the heater. If you make it well insulated, you can even use it to transport.
I have had mixed results with temperature controllers. The worst thing to happen is for it to fail with the heat on. I burnt 2 5 gallon pails of honey in a honey heater cabinet when the controller failed to shut the heater off. I have recently put together and Arduino controller from parts off of eBay for like $25 with 3 sensors to hopefully prevent reliving my overheating incident. A lot of the cheap controllers have poor regulation as well.
Oh, and just like incubating chicken eggs, don't forget to add a wet sponge for humidity.