This is why an op-amp has a high input impedance.
The temperature probe connections have a resistance of around 1000k. That's pretty high, which when coupled with the polarity markings indicates that there is an op-amp on the board and the temperature probe is a low current voltage source. Also known as a thermocouple.
This means I can now simulate the presence of the temperature probe by supplying an appropriate voltage(not sure how big yet though). By simulating the presence of the thermocouple I can test if the electronics will turn off the heater current at some point which means that it was just the thermocouple that failed. The outer braid of the thermocouple has failed where it enters the remains of the aluminium so that makes me think that something went badly wrong with the thermocouple.
While I had the multimeter out I also measured the heater coil's resistance- this came out at about 700k. So with a little math we can calculate the current flowing through the coil and also the wattage(not really that important but might be interesting to see how much power the electronics use).
I=230/700k (Pretty sure 230V isn't RMS but I know it isn't Peak to Peak so it shouldn't give us a number that is too high)
I=230/700 000 (Now in SI units)
I=0.003288571A (Seems very very low ???)
Now for power consumption:
This is clearly wrong so I decided to check again... It turns out that my fingers have a resistance of around 700k ohms and it was this resistance I measured. The heating coil appears as an open circuit so I think I'm going to have to melt out the remains of the Aluminium block and get a closer look.