Share tips and tricks to keep people from throwing out that broken item. Repair before replace!
Depends on how handy you are at fixing things. I have fixed similar things when the motherboard has fried, and is not available, by wiring in a PID (a fancy temperature controller).
It could be as simple as a burned wire. I would urge you not to do any electrical repairs yourself unless you are confident about your skills.
Exactly this. It is of course possible to fix anything, given spares, skills and time, but if you have to ask, then you probably don't have the skills already.
Kitchen equipment tends to be quite simple to repair - burned out heating elements generally just unscrew, motors and valves in washing machines tend to be modular, and just swap out - but if you're not confident with a multimeter then you won't be able to diagnose it. They tend to be high-power appliances too, which are the riskiest when things go wrong.
If the alternative to fixing it is just to replace it, then feel free to take it to bits and see if you can decide what's wrong. If there's very obviously a burned-out part and it's easy to swap out, then go for it. Otherwise, you can learn about that the parts are and how it all fits together - every day is a school day.