If you’re willing to do that why not just buy a sous vide? There are $50-60 ones available. I’m guessing cause you want to code the control, but just saying because there was a time when I couldn’t find one for less than about $300 but they’re more affordable now.
I actually already have one that works fine. It's less about cooking better chicken, and more curiosity about the software, PID algorithms, etc. The AC relay isn't all that interesting to me, so I'd be happy to treat it as a black box.
