Not very hot, and it needs to be applied for a longer time.
Shamelessly stealing this link from the mentioned thread: https://en.m.wikipedia.org/wiki/Cauterization#Electrocautery
Notice the following phrase:
- "The electrically produced heat in this process inherently can do numerous things to the tissue, depending on the waveform and power level, including cauterize, coagulate, cut, and dry (desiccate)."
All I have further is a personal experience with a local operation using an electrified knife (which isnt mentioned in the wiki). The knife was first put on a high setting and cut through the skin and flesh smoothly, but the wound bled a lot. Then when all the necessary cuts were made they used cauterization instead of sutures. They did this by lowering the temperature and pressing it to the wound for several seconds, and re-applying it if it still bled.
High temperatures are worse as they affect more than the area you use it on. While this will stop the bleeding at the area* you apply it too its only because the blood vessles are destroyed and unable to supply blood there anymore. The tissue surrounding it will become necrotic without expert medical care and die off while likely causing massive infections that have a high chance of killing you without modern medicine. cutting off a limb this way would likely cause Gangreen, which will necessitate you to... amputate the limb before it reaches the torso... which is kind of a problem if your limb removal method is what causes it.
Also note that the cauterization link does mention large blood vessles still need other methods of closing them off.
*I used to think it made local bleeding worse but that was wrong.