エアコンつけてるのに暑い。って英語でなんて言うの？

All sentences can be used here.

They are simple sentences used to say that its hot even with the AC on.

'despite' - when something is not affected or changed by anything.

I hope this helps :)

Unfortunately, sometimes the AC does not work properly, or the system cannot keep up with the soaring temperatures. In that case, one of the above expressions may be suitable. Cooking on a hot day can be quite uncomfortable.

No match means that one thing cannot succeed against something else.
The AC is not strong enough for this heat.

1. Even though the AC is on, I am still feeling hot.
   The phrase "even though' means "in spite of the fact that"
   This sentence is saying "in spite of the fact that the ACis on, I am still feeling hot."
   Examples:-
   Even though he studied hard, he still failed his exams.
   Even though she was warned, she still broke the law.

sweating bullets: is a common phrase used by English speaking people to indicate that they're sweating a lot and that the environment they're in is very hot.
The second phrase explains how the heat coming from the stove that's cooking the food is very strong that the AC isn't cooling it fast enough.

Hope this helps!