My Pete lived in 75-80 degree indoor temps for a while at our last place; and when it got towards 80 he did tend to slow down or take more breaks from playing. Occassionally it would start inching higher than that, or the power went out all-together, and I had to get him some chilly things to cuddle with since he refused to sit on smooth surfaces.
I found a good trick for higher-end temps is to take a pillow case and place a cold pack inside it, then folding over the extra material. Peter loved this as it wasn’t too chilly because the extra folded material was on top, but as it thawed it became a sort-of bunny-water-bed that was still cooler than most of the room. When it thawed too much I’d simply take it out of the pillowcase and stick it back in the freezer for a while. He’s not a chewer though… so it would depend on your bunny’s habits, and might still be good to monitor it anyway. Frozen water-bottles stuck in socks also make for good cool-cuddle buddies for the bun, and are a bit more secure from potential bunny-puncturing.