Potentiometer overheating
Power is equal to the square of the voltage divided by the resistance, or $$P=\frac{V^2}{R} $$

For 12 volts and 10k, P = .0144 watts, which certainly will not overheat.

The thing is, you are not applying the voltage across the fixed leads of the pot. Instead, you are applying voltage to the wiper, and as you change the wiper position you change the resistance. As the resisistance goes down (the shaft approaches one limit) the power will go up. In the worst case, if you turn the pot all the way to its limit, the resistance will nominally become zero, and the power (nominally) infinite.

So don't do it. Or, if you must, put a fixed resistor in series with the pot so that the minimum resistance produces an acceptably low power.