I have always preached that the division of DE into dQ vs dW in the first
law of Thermo is not unique, and that teachers should not hold students'
to their own pet "ratio divisionis" for each individual situation. It is
important only that one use an inclusive accounting method which correctly
tracks all energy changes to the system under consideration, however one
chooses to label and group various mechanisms of energy change - a
question only of choosing a convenient taxonomy (we have ploughed this
ground before, in threads concerning dw in work energy theorems vs dw in
the first thermo law.)
But, whatever taxonomy we use in exercising the first law, engineering and
daily life demand that we recognize that a system can (and definitely
will) undergo an energy change soley because of a temperature difference
between it and its environment (eg., that's why we insulate our homes - we
seek adiabatic conditions to minimize this temperature-driven process).
It does no harm (and is useful) to give a name to such processes and even
to model them as the transfer of a quantity (even if only mathematical)
called heat.
The only difficulty I see is that caused by artificial first law test
problems concocted solely to force students into the author's (or
teacher's) chosen taxonomy. This is analogous to insisting on THE five
causes of the American civil war. While it may be conversationally useful
to choose a common taxonomy, realize (and say) that it is a _choice_.
(Who can think of other places where we force students into an arbitrary
taxonomy?)