Is it acceptable to say
This determines how strongly heat is transferred from A to B.
One of the definitions of "strongly" is
to a great degree or extent
So the answer to the question above seems to be yes.
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It is not “wrong” to refer to how strongly heat is transferred, but it doesn’t fit well here. It has a different meaning that is not commonly applied to a transfer. When we describe a process we are more likely to talk about how well, how completely or how quickly the process occurs, not how strongly it occurs. We are usually discussing “degree” not discussing “strength”.
For example, strongly is not a good substitute for the words in bold in these sentences:
How well does heat transfer through water?
Does stirring influence how completely the crystals dissolve?
The temperature influences how well the concrete sets overnight.
Warm days change how quickly the green leaves turn orange.