If the fish are fine then it's nothing to worry about. Lots of fish can adapt and you don't have any over-sensitive fish. If you don't already have one, adding an airstone will help get oxygen into the tank which is important certainly for the cories.
My tank is currently at 82 as well and I have various fish (in my profile).
At 82 degrees, the water will have less oxygen like Cheese Specialist said. Any kind of surface agitation will help get oxygen into the water. If you see the platies gulping for air at the surface, then you need more surface agitation. The platy seems like a good way to measure, since the betta fish takes air already even if there is oxygen in the water.