35 is....hot....
Then again, the norm here is 30 these days at the peak of summer. Both Syrian hams have taken to passing out all over the place in the strangest positions. And almost always out on top of something not inside a house.
Best recommends I've seen are taking a dish kept in the fridge and putting it in the cage for them to lie on. Tiles and cool rocks work as well. Keep the air moving with a fan, but not directly blowing on the cage. I can always tell the circulation of air in the room by where the hammies sleep, lol
Both my six month old Syrian and the new baby still exercise, eat and come out, but some days? Well we all have dog days so to speak...
Retopping off the water with cold water also helps.
I tend not to worry too much. They're Syrian hamsters. They were discovered outside of Allepo Syria which is very hot in the daytime and very cool at night out in the desert areas. Even though mine are both long hairs, (which was a later genetic development) I figure they were built for Syria, so a heatwave is something they seem to take in stride. I agree 35 is a bit on the too hot side if it were the norm....
Your hamster sounds fine. The tips above might help.....