Is non use of the APU a legal thing or part of the Ts and cs which vary by airfield?
As you have noted some airports are very "hot"
on APU useage based on emissions and noise poicy, some less so..There's also sometimes a question (from the airlines POV) of whether it is cheaper/allowable to run the APU or shut it down and instead pay for airport supplied ground air and electrics.. Fundamentally it varies from airport to airport (we carry the company preferred preference for each airport in our route network in our onboard documentation).
That said you may have use bit of discretion and engage in a bit of negotiation if dealing with high cabin temps.