The water shouldn't cool down so quickly ... if it's just this hot during mid day - I would suggest to get a fan and blow it over the top of your opened tank to try to keep it cooled. And, no lights! ...
Try to keep your shades down to keep the heat out as much as possible.
yes. ice-cubes... but not so many as to put the fish into shock. Bettas do like heat, even in the high 80s they'll be fine. Try not to stress to much - try to keep your place cool, maybe open all the windows and place fans to get things to cross ventilate... if that's possible, do it... if not... don't stress.
before the conditioner accident - how was the betta responding to the 90 heat? any lethargy? not eating? ... or acting normal?