Don't kill the typist. I've found some definitions. Vote for one or none of
the above.
Bob Carlson
a. Symon, Mechanics 3rd Edition
If we regard a body as composed of atoms and molecules, its heat energy turns
out to be kinetic and potential energy of random motion of its atoms and
molecules.
b. Resnick, Halliday, Krane, Physics 4th Edition
Heat is energy that flows between a system and its environment by virtue of a
temperature difference between them.
c. Feynman, Lectures on Physics
Volume I
4-4 Other forms of energy
It turns out that with thermometers you can find out that, in fact, the
spring or lever is warmer, and that there is really an increase of kinetic
energy by a definite amount. We call this form of energy heat energy, but we
know that it is really not a new form, it is just kinetic energy - internal
motion.
Volume II
The differential equation of heat flow
You know that if you take a slab of material and heat one face to temperature
T2 and cool the other to a different temperature T1, the heat will flow
through the material from T2 to T1.
d. Tipler, Physics, 3rd Edition
Heat is energy that is transferred from on object to another because of a
difference in temperature.
e. CRC Handbook of Chemistry and Physics
Heat - Energy transferred by a thermal process.
f. Serway, Physics, 3rd Edition
There is a major distinction between concepts of heat and the internal energy
of a substance. The word heat should be used only when describing energy
transferred from on place to another. That is, heat flow is energy transfer
that takes place as a consequence of temperature differences only. On the
other hand, internal energy is the energy a substance has because of its
temperature.