The temperature is managed by a controller I purchased off Amazon, I believe Inkbird brand. I set the temp range I want it to maintain, the power supply for my cooler plugs into the Inkbird and the Inkbird plugs into the wall. Very simple. Mine only does one function. You have to set it to either cool or heat mode. I dont have to worry about the closet getting too cold and dont need a heating function.
I built the peltier system myself so I'm not sure about what options are available on the market for those. I can go into further detail on the system if anyone is curious.