Also, the Weller in question (WECP 20) isn’t doing PID. There is a potentiometer knob and a resistive temperature sensing element in the iron that together either turn heating on or off. It doesn’t get much simpler than that. Full schematics are readily available online.
Heating is either on or of, but it's on the order of "a few times per second". The heating action is connected to a small indicator lamp that lights up when the transformer is pushing power through the iron. You can hear the transformer buzzing briefly every few seconds to keep the tip around the set temperature. Touch the tip to a large thermal mass, and the transformer buzzes continuously. I expect there is a Schmitt trigger or a simple comparator in the control board that is in charge of the heating action. Again, check out the schematics to see how simple it is.
> Do tips not have an ideal voltage for efficiently emitting IR?
What do you mean by emitting IR? A soldering iron doesn't melt tin by radiative heating. You make physical contact with whatever you are intending to heat.
Are you perhaps thinking of Curie point soldering (or inductive heating) [0]? Those employ a much more complex process. My Weller goes by the "make the pointy metal stick reasonably hot" principle.
[0] https://www.metcal.com/wp-content/uploads/2021/11/how-it-wor...
I'm not certain about how dumb something is if no code is involved. Just might be very smart to be able to leverage fundamental physics in such a way.
That said, analog processing can be subtle. Have you disassembled the thermostat to see how it implements PID?