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Let me paraphrase JohnD (see below) in order to be corrected,
if necessary.
There are no advantages in emphasizing that heat is "energy in
transfer".
Heat is a form of energy.
Thermal energy is heat.
It is not wrong to say that the heat lost by an object A is later
present in objects B or C. The caloric analogy is not totally
wrong. Heat can flow but it is not a material substance.
There are more important issues to deal with; some students
are not aware of the fundamental difference between heat and
temperature.
Trying to avoid dS=dQ/T may be challenging to
some creative thinkers but many teachers are used to it. They
need to be persuaded to abandon this macroscopic approach.