I agree with Leigh that precision in language is necessary in physics.
I believe that this precision is necessary for students who should be
in the process of learning to think with abstract concepts. Thermo-
dynamics is over 100 years old, its language can be precise at no cost.
If teaching is imprecise and the teacher uses terms such as thermal energy,
internal energy, heat and maybe others as synonymous, the student is not
being taught well.
In thermodynamics, changes in internal energy are defined unambiguously by
the work done on a simple substance in an adiabatic process. Internal
energy is an empirical concept. Heat (transfer) is then defined via the
first law of thermodynamics for a general process without the adiabatic
restriction: Q = deltaU - W. Heat, Q in that equation, is indeed energy.
The equation also goes by the name of the Principle of Conservation of
Energy. Heat does flow as it transfers across one surface at x1 and then
across another at x2 such as in conduction. It is just that it is not a
flow of a substance or of matter. Maxwell apparently could not think of
electromagnetic waves without a material medium to vibrate, and invented
an aether, but it was not necessary, there could be waves without a
material medium.
A final point is to say that since thermodynamics can stand on its own
with its concepts and postulates it is not necessary to bring in to
discussions of clarification the subject of atoms and molecules. One of
the beauties of this subject is that the microscopic make-up of the
substances is not relevant and it also leads to its great generality
in applicability.