Alright! It's done!
I decided to chicken out and keep it super simple - skipped the switch altogether. The only situation when it would be needed is when I want to run the fan with temperature below the trigger point. Like when sbd is cooking and smoke density reaches -cough- certain levels. Note the little thermistor sticking out cheekily.
In that case I can just lower the starting point which takes just a couple of seconds. Long push -- push push push push (it increments in 1/10 degrees) push push push push and there.
I used the existing screw hole to attach the temp controller to the fan casing. No obvious modifications in case I regret stuff and want to do something else.
Right now I have it set to turn on at 28C (actually it turns on at 28.1) and off at 26.5C. Works really well so far!
As I had mentioned somewhere else, I can spot the road when opening a drawer.
I figured, when you've got lemons... so I covered it with chicken wire and some coarse cloth.
So now the critters have some resistance to entering the cave, and I only need to open the drawer a bit to get some cool air to flow in.
We'll see how it works out, but should be a good way to keep the temps a bit lower than what they would be without it.
Thank you!