Heat
Energy transferred between bodies because of a temperature difference — an amount, measured in joules, not a substance.
Definition
Heat is energy in transit, flowing spontaneously from a hotter body to a colder one purely because of their temperature difference. It is an amount of energy, measured in joules, and it is one of the two ways (the other being work) that a system's internal energy can change. Heat is not a property a body 'contains'; a body holds internal energy, and heat is the name for energy crossing a boundary by thermal means.
The modern understanding overturned the eighteenth-century caloric theory, which treated heat as a conserved fluid. Rumford's cannon-boring experiment and Joule's paddle-wheel measurements showed instead that heat is interconvertible with mechanical work at a fixed exchange rate — the mechanical equivalent of heat — establishing heat as a form of energy.
Heat must be distinguished sharply from temperature: temperature is an intensity that sets the direction of flow, while heat is the quantity that flows. Confusing the two is the most common error in the subject.