I heard this flight give the in-range call last night; said the APU was deferred and pax were hot. The voice on the radio sounded exasperated! Guess the sit in PBI and the short hop to SFB never quite got the cabin cooled-down. To make matters worse, SFB made them wait another 15 min on the ground to park; props to the 80 crew that landed before them refusing to park until PBI got parked. I can't imagine the pax disbelief when they got cx'd part-way into their trip...what a mess that must have been at midnight last night!!