Oil temp is important, but there are other aspects. Thermal shock of setting high power on a cold engine or shutting down a hot engine can cause compressor or turbine rub and permanent performance loss.
Also, shutting down an engine when it's still really hot can result in fuel or oil coking due to the thermal soak-back - both can have bad long term results.
I'm referring of course to large turbine engines - no idea how susceptible turboprops might be.