Cooling down the tank is okay, but don't cool it down too fast! Too fast (even if it stays within the betta's normal range) will put them in shock, and they can die. Bettas are hardy little guys, bear in mind that they come from Thailand and other south-east asian countries, and they have extremely hot summers there. The water in some of the rice paddies and ponds they live in with stagnant water become quite warm too, and no one puts ice cubes out there for the fish.
I've known someone who has kept bettas in outdoors tanks in Florida. The summers here are also extremely hot and I'm sure that water was well above 90 some days. The bettas went through that just fine. It's not so much a hot temperature that kills the betta, its the rapid change I think that does it.