If you have a broken EQ that runs too hot to use, no matter what the dial says, are crazy or desperate, well out of warranty and overseas like me, then this may be worth a try. Clearly, it is a last ditch technique when the EQ would otherwise be thrown out. You'll need a PWM DC controller board (anything rated +24v +50W will work fine - a few dollars on ebay)
After about 5 years of reliable service, my first EQ got hotter and hotter over a week - same dial setting (190c)..long story short, the thermocouple weld had failed - I pulled it out to confirm. Arizer says "safety" and won't sell me a replacement heater/thermocouple unit. So I whipped out the soldering iron.
The heater element resistance cold was about 7 ohm using a crappy old multimeter so at 12v will draw less than 2A max for 24 watts. Well within spec for a cheap chinese PWM controller board I had lying around. The idea with pulse width modulation is to turn the input DC supply on and off really fast but to control the ratio of total on to total off as you turn the PWM dial down. For example, if the total off period is 50% of the time, the heater element will draw 2A 50% of the time on average so will run at about 12W. The rapid switching is not likely to hurt the heater element, particularly if it's +thousands of times a second.
So I wired it so the PWM input is the 12V DC from the wall wart, and the load is the heater circuit.
Do not try this at home kids. The potentiometer shaft sticks out from an ugly hole in the shroud. It looks really, really awful.
I plugged it into a wattmeter and left it running after turning the dial on the PWM board so it was consuming 18w - too hot - I'm working my way down - at about 11W it works much like it used to - despite the lack of temperature set point. It's just pumping out 11W and in thermal equilibrium most of the time except when my occasional (slow) toke drops the temperature a bit - probably more than it did when it had a working thermocouple. Bottom line is that not only does it work, but it works surprisingly well so far. Takes a long time to get heat soaked but I can turn it up and return to the 11W setting when it's ready. I'll report back after a few days. I'm waiting on a probe so I'll be able to get some temperature readings. At 11W, I am getting excellent looking ABV - no scorching but uniformly and well toasted - same as when it was working properly at about 190 on the dial. I actually could not really care what the dial says - it hits pretty much as well - although dialing it in involved 3 bowls in half an hour so I might just be befuddled.
Google tells me that they can be rewelded using a 12v car battery and a carbon brush electrode to soak up oxygen! Too late to try that now - but I now have a sort of log vape that I can use all my DDave kit on.
YMMV