Hello again,
Well this would be much like a room thermostat, except you're would be measuring say the bottom plate and when it gets to a temperature that correlates to the temperature of the coffee then you break the connection to the heater element. This would take a small circuit that is set up to measure and turn off. Eventually if you wanted to use a thermal switch you could do that, but to determine what temperature you'd have to experiment a little.
I find my coffee to be around 125 degrees F when it is served, but the 'hot plate' under your coffee cup will have to be hotter than that.
The measurement circuit could be a thermistor connected to a comparator, and a couple other small parts. The drive switch could be a MOSFET.