So here's an awfully uninformed question that will probably get me laughed at by actual engineers (as in, not 'software engineers' like myself - and yes Canadians please bite your tongues, I've heard your shpiel by now): when you have a more powerful computer to work with, isn't it much easier to just derive some regression parameters and call it a day?

My use case: I have this home-build growhouse that I use to start my seedlings in at the end of winter (and as a fermentation chamber for wine). It's controlled by a Raspberry Pi and as inputs I have 4 groups of LED grow lights, a 30w heating element, a fan that draws warm air out of the box and thus brings the temperature within the box towards ambient temperature, and DHT22 sensors that measure temperature and humidity inside and outside the box. The goal is to keep temperature as close to a certain target temperature as possible, keeping in mind that I want the lights to be on for a certain nr of hours per day and the lights give off so much heat that they will pretty much always make the temperature go over the target (so the fan then needs to bring it down again). It's easy to get this working the naive way with an hysteresis of say +/- 2 degrees (which is fine for my purposes), but the nerd inside me sees it as a game to make that band smaller. So I've been reading up on PID controllers and dear baby jesus I can't even work out how I'd get started. So the pragmatic part of my brain goes 'just run it for a few weeks with incremental inputs between 15 and 35 degrees (C, of course), measure the responses, toss all measurements into R and derive some regression parameters'.

Does anyone do this in industry? Probably not because everywhere I've asked, everybody's who's ever done real work on this uses PID controllers - but is that because they're easier to build on microprocessors (i.e., need less number crunching)?