At 8am in PHL today when it was already pushing 80 outside, the E175 I boarded had no AC. First time I can recall this happening in...well, I can't recall a time when AC wasn't functional at the gate on a hot day.
The FA and Captain told us the AC isn't working until the engines start. It wasn't to the point of unbearable, and sure enough when we pushed back and the engines spooled up the AC was a welcome Arctic blast.
that would be true if the APU is inoperative, however, cold air should be available at the gate via a conditioned air cart or dedicated hose at the jetway. The captain's responsibility is to make sure the aircraft is a reasonable (i.e. safe) temperature for passengers. If it is not, then do not permit boarding.