Airbus350, silver and others,
There are prescribed oil temp limits which must be adhered to before takeoff, whether single engine or not.
Further as I recall on shut down the engine needs to have been in start/feather for 1 minute before bejng shut down.
On a cold day and first flight the engines can take some time to come up to the correct temp prior to flight. Other than that it is not a problem as the short turnarounds do not allow the engines to cool down that much.
After landing the engine is put into start feather for 1 min prior to shut down wheather on stand or during taxi in.
All engine manufacturers have their own procedures which should (and in in this case are) be followed. Your plane and procedures will be different and you should follow them.
GE do not follow RR etc.so do not presume that just because procedures do not follow your company sops they are wrong.
This is a non issue.