Definition: Heat energy (or just heat) is a form of energy which transfers among particles in a substance (or system) by means of kinetic energy of those particle. In other words, under kinetic theory, the heat is transfered by particles bouncing into each other.
In physical equations, the amount of heat transferred is usually denoted with the symbol Q.
Heat vs. Temperature
Note this crucial component to the above definition:
Heat always refers to the transfer of energy between systems (or bodies), not to energy contained within the systems (or bodies).