Why do some turboprop engines require motoring after shut down?
Rotating the propeller of the Cessna 441 Conquest II is to cool the Garrett TPE331 engine in the aircraft. From airliners.net


  On the Garrett TPE331's we were trained to spin the props after shutdown to get cooling air flowing through the engine, this was done right after shutdown. Half an hour after we did the prop spins we had go back out to the aircraft and rotate the propellers one blade width. Moving the prop one blade width rotated the engine one half turn, this was to prevent the shaft from sagging as the engine cooled causing turbine blades to rub.


The reason is given as:


  Direct drive turbo prop engines sometimes require this to remove residual heat from the engine because once the prop stops turning, so does the engine. When the pilot turns the prop, depending on the gear ratio, he is actually spinning the engine very fast. This helps move some of the heat out of the engine.