Lets face facts here folks.
The Commander of the flight really has no authority until the doors are closed, and push back is commenced, in spite of what some junior First Officers, CC or outsiders might think.
IE: the groung staff have this requirement while the doors are open, and that is where the fault lies.
The Captain (or indeed the First Officer or CC) can huff and puff all they like, but those are the facts.
If, OTOH, the Captain was to say....I'm not taking it until its cooled off inside... then he might well have some tall explaining to do to airline management, union or no union, provided of course, that the aeroplane was otherwise serviceable according to the MEL.
In short, like it or lump it.