Fixed wing pilot only here so indulge me
Currently reading ‘ guns & gunships’ by Mark Garrison who flew the UH1 in Vietnam
He mentions the common practice of hot refueling between sorties then, it saved time and he emphasized that it reduced the possibility of a hot start with a brief shut down leaving you with high residual EGT prior to restarting
That all makes sense and of course it’s easier on the battery and fewer engine cycles
Just out of curiosity though, can you not motor a helicopter turbine with fuel off to lower EGT prior to fuel on ?