In the World of Tweed we are told to shutdown the APU after engine shutdown and EXT PWR is connected. We are then permitted to start it again when before Pax board.....
However, on the day it up to the operating crew(i.e. CPT) as to the best course of action. Frying your Cabin crew and cleaners in 35 degree heat on a summer turnaround in greece whilst still expecting a fast turn is just stupid. As is chilling your fare paying pax at 4:00am on the first rotation as we wait for boarding to finish.
Common sense prevails on the line - but the company, in good faith, is trying to reduce fuel consumption and latterly reduce carbon emissions so therefore asks us to assist by either shutting the APU down or when EXTPWR unavailable by running the APU with the bleed valve closed resulting in a lower APU EGT (757/767) and lower burn.
As they say in the movies lately with the fuel price as it was "all other concerns are secondary" Maint. cycles etc... have been ignored and fuel price has been the driver.