I don't know what software you're using, but tuning a feedback loop for something like a thermocouple is typically pretty easy to do in software. Doing it in hardware is where it becomes more involved. You only need the proportional and integral part of the feedback loop, the derivative doesn't really do much for you and you can disregard it. In any case, a proportional-integral feedback loop can be done in software with just a few lines of code. It's actually surprising how easy it is when using a minimal approach.
For example, here's the formula in discrete terms for one I did recently,
Vc+1 = Vc + ( Vref - Vfb ) / (5 * Vref -2)
Vref is a constant, Vfb is the feedback voltage and Vc is the control input. You can see it only takes a few lines of code for the math and a few lines above and below to grab and send the data.
The interesting thing is, in hardware this is a huge task to accomplish requiring the use of differential equations and advanced mathematical methods to find component values. Doing it digitally in software greatly simplifies the task.