I'm currently working on a version of this for my local open source hardware group. But at this point I'm working with the $10 Mainstays hot plate from Walmart, topped with a circular saw blade. See attached pics.
The idea I had was to use an MCU-controlled SSR to cycle the AC power on and off. The cycle would repeat every 5 seconds, and average power would be determined by the duty cycle (i.e 2 seconds ON, 3 seconds OFF). The duty cycle will be adjustable in 100 steps (50ms increments). That's my equivalent of a variac or rheostat.
I'm going to use a TM-902C thermocouple to follow the temperature, and try to develop a sequence of duty cycle steps that produce the right temperature profile. Then that exact sequence could be repeated without the need for any temperature feedback.
The "controller" will have a rotary encoder and two-digit display through which the duty cycle can be changed. I'm currently writing software (in assembler) for a TI MSP430 processor (because that's what I have on hand). But the SSR won't arrive for a week. So it will be a while before I have an idea of whether this will work.
This wouldn't require modifying the hot plate, and I think the controller could also be used with an unmodified toaster oven. The cycle period doesn't have to be 5 seconds. It could be anything.
I'll be happy to share any of this. I just don't know at this point whether there is anything useful to share. And someone would probably need to translate the code to Arduino. All my code is in the interrupt service routine. The processor sleeps between interrupts. I don't know how well that works in Arduino land.
Apparently a lot of people perfer hot plates over toaster ovens. Apparently they get more consistent results, and fewer burned boards or parts. But I don't see how that could be the case without some control over temperature. Anyway, we will see.
If you want temperature feedback, the Rocketscream Tiny controller looks interesting, at a good price.