No, Sir; as I said above, it's the delta T resulting from the change in pressure between the fan and the core, which acts as a restriction.
Pushing air compresses and therefore heats it. Passing that air through a cold core maximizes delta T, because of the extra heating between fan and core. Once the air passes through the core, pressure and therefore temperature drops. If that core is hot, then the pressure drop works against you in heating the air. The harder you push, the greater the effect and the less efficiently it will draw heat from the core.
Conversely, if you draw the air through a cold core then the pressure DROP between core and fan reduces delta T and makes it less efficient. Again; the harder you run the fan, the bigger the pressure drop and the worse it performs. If the core is hot, then the air, being colder due to the pressure drop, sees a bigger temperature change between itself and the core; delta T is larger and efficiency is improved.
This is why I suggested the experiment above, so you can see and feel the difference for yourself. It's not trivial!
If the BTus are free then of course CFM costs more.