Wow.
OP....
Where are you even located in the world where it is so hot + humid this time of year....??!
Anyways she owes you more than an apology for being a 1/2 Hr. late.
She owes you money too.
Also, you need to be comfortable at work.
If she won’t let you turn on the A/C, then she certainly cannot fault you for opening up the balcony doors (though make sure to ALWAYS watch your charge when they are open!)