I expected this to be a complex job but it wasn't. I definitely wasn't looking forward to paying a callout fee to plumber or electrician. So I fetched my toolbox and my multimeter and went for it.
Switched off the isolation switch, removed the cover. Something was immediately apparent, there was what could only be described as a scorch mark on the Live wire and the thermostat. I tested the voltage, all 240 volts were arriving safely at the thermostat but it could still mean the heating element is the one with a problem. So I removed the thermostat and tested it for continuity and the test was negative, no continuity.
The element had continuity so I took that to mean the thermostat is the issue. I went to Builders warehouse, got a new one. I put it in, connected all the wires, put on the isolation switch and it immediately started with that familiar hum of a kettle after you put it on. I assume this means it's fixed. I still don't know what caused the issue with the thermostat though. I expect there will be hot water soon.
Second DIY job getting knocked out in a short time. I don't know if I'm getting better or it's just easy jobs. who knows. I'm glad it worked though.