Definition of "heat" (Webster, 1913):

 A force in nature which is recognized in various effects,but especially in the phenomena of fusion and evaporation,and which, as manifested in fire, the sun's rays, mechanical action, chemical combination, etc., becomes directly known to us through the sense of feeling. In its nature heat is a mode of motion, being in general a form of molecular disturbance or vibration. It was formerly supposed to be a subtile, imponderable fluid, to which was given the name caloric.

This is thoroughly gratifying to read!

If I were to give a shorter definition, I would say: "a force in nature which is perceived by the sense of feeling as warmth when moderate and as a burning sensation when excessive".