Difference between heat, thermal energy, and temperature

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This isn't really a homework question per se. I'm studying for my MCAT and I'm having trouble trying to firmly get down some of the concepts in thermodynamics.

As far as I know, heat is the means of energy transfer that isn't work from one substance to another due to a difference in temperature between the two substances.

Thermal energy is the total amount of kinetic and potential energy in a substance.

Temperature is the average (per particle) amount of kinetic and potential energy in a substance.

So something that has a lower temperature, like a big chunk of ice, may have more thermal energy than something like a small heated nail.

Am I on the right track? I'm not too sure whether temperature/thermal energy is a measure of potential energy and kinetic energy, or just one or the other.

Thanks for your help.
 
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Thermal energy and temperature refer to kinetic energy, and not potential energy. For example, it when you add heat to ice at 0oC, the heat does not change the thermal energy or temperature of the ice. Instead the heat changes the ice into water, increasing the potential energy of the water molecules.
 
Is not thermal energy also related to the potential energy of the molecules?
 
It depends what you mean by thermal energy (I'm not so sure this is a well defined term). Certainly the internal energy and enthalpy of molecules are dependent on both the kinetic and potential energy of the molecules.