unless the rotors are at something mad like 200degC (guess) then I really doubt there would be much transfer to the air.... ok it could soak the manifold and then soak the cooler water circuit but thats a little tenuous imho.
Its simple fizzicks of pushing more air than is needed into the manifold/engine
looking at this the wrong way, it's the compression of air that get's the nose hot, not the other way round.
cooling that end of the charger would not be a bad idea, but it's not going to make any odds to the air temps per say, it will however help the chargers bearings and rotor clearances.