Control overshooting
A P-only (proportional-only) controller will back off the power as the setpoint is approached but, generally, will settle down a little below setpoint unless you add an offset.
A PI (proportional-integral) controller's integral action will correct the error over time and regulate to setpoint. With good tuning it also gives the fastest heat-up time.
You might find my answer to Understanding the flow of a PI Controller? useful.

Notes:
The system overshoots because the stove has to be hotter than the water if heat is to be transferred. Once the setpoint has been reached the stored energy of the stove is transferred to the pot until equilibrium temperatures are reached. The heat capacity of water isn't an issue other than its value relative to that of the stove determines the final temperature as the excess energy will be shared between them.