Yes, rotating the prop by hand shortly after shutdown is done to minimize the effect of shaft bow by ventilating the engine with cooler air.
Might be splitting hairs, but hand rotating the prop doesn't effectively ventilate the engine relative to the rotation speed even in the final phases of shut down, which is when most of the hot gases would be vented. Plus the number of recommended rotations is negligible in the grand scheme of things. (Three full rotations, if I remember correctly?)
Thermal bowing is at its worst around twenty to twenty-five minutes after shut down, as the warmer air has had time to rise, and cooler air to sink. Rotating the prop after about ten minutes mitigates the bowing by mixing the air again and leaving it sat in a different position. It's moot after approximately an hour as temperatures in the casing and shaft will have equalised. You often see eager crews leap out, spin the prop a minute or two after shutdown and think "job done". You can pretty much guarantee in a short turn around there is no further check of the engine for thermal bowing before starting again... I contribute this to the 'venting theory'.