OP, make an effort to find the schematic for your 936 clone controller board. Or just sketch it out. Guessing is not going to work well.
It looks just like the (cheaper build) Atten 936 here: https://www.eevblog.com/forum/reviews/atten-936b-another-hakko-clone/
But your smaller resistors are 1/8W not 1/4W. I found a schematic sorta like how it is for architecture- three zener diodes. Two make +/-7.5V for the op-amp power and a 4.3V for the reference voltage. I think some use thermocouple others use RTD as the sensor.
That circuit looks like it uses a floating 1/2 voltage node (thermistor/thermocouple return) which would get destroyed if there was ever a heater to temperature sensor fault.
If you have a short in the handle/heating element it would explain your smoke. I'd draw the schematic but no time and can't read all the parts.
And the winner of a gift from life or beyond life is floobydust. In india there is ancient belief that life has gifts from higher realms discoverable through life. I like to imagine floobydust earned that by presenting the gift of suggestion that made me think to try the simplest thing.
how ironic that for maybe years this sat for parts and all it needed was a new handle/thermistor. And I even tested the heating element resistance as mentioned earlier. Both identical handles but 1 element 19 ohms, the new spare 12. But the thermistor pins on the old handle tested wildly all over the place, jumping from 0.9 ohm to 10 and all in between from seemingly breathing in the same room. While new spare was 0.9 steady at idle room temp.
Noticed the old handles pcb pads looked crusty, like a white flux film was on some. Poor solder on 1 side on every through hole joint. But I fear If the thermistor is burnt I cant get it out of thd tube over the element. So even if I make sure the joints are better, it risks smoking r1 and r2.
By the way? Replacing all the parts I did wasnt needed. I burnt like 5 of both valus resistors trying to repair the board over the years. Wait, I do think I needed to replace the lm358. But everything else was good. Zeners were originally 7.5 im pretty sure. Well the reason I feel that way most is that the board started to smoke r1 and r2 after I put 5v zeners. Only not using that handle changed then. And now it works!
Tested voltage across resistor r1 (before trying new handlree, in the 4 secionds it took me to probe with dmm and power off a woft of smoke came off both resistors) I got 0.130 and if my math was right 0.1a would be the draw for 330ohm on 33v. But yeah new handle and the only semi hot parts are the 2 biggest resistors. R6 and r14. At 30c.
Thanks to everybody who took a crack and offered perspective.
This station is back in business after a long hiatus. Its thankful I bet.
Im thankful to not smell more burning resistors.