Answer:
Heat travels from a higher concentration of heat to lower concentration of heat. The heat will diffuse to the cooler areas, which means the handle would be heated, and the cook feels the burn since the heat will travel to him because of the temperature difference between him and the pot.
Your voltmeter and your teacher are both right, but the water analogy of electricity can only go so far. One big drawback is that, unlike with water, there is no absolute voltage. .... Wherever you put the black lead is defined as "0V". .... flowing (i.e. the circuit is broken) you will not get this change in voltage.
