Pedantic twitch. You wouldn't need the "I"(integral) in PID as we can only drive the system one way. You hardly need the "P"(proportional) either, if you are just trying to figure out when to shut off the power. That leaves shutting off the power based on how fast the water is heating up. So really just "D"(derivative) control. Which is super simple. ... and that is even assuming that there is enough thermal mass in the heating coil compared to the thermal mass of the water to ever make a difference.

It is gotten to the point where I get a twitch whenever I see someone refer to the PID concept. In most cases it gets used in an inappropriate way.