Rabbits don't sweat either but you can spritz their ears and put them in front of a fan. Get them used to a fan a low setting. Guinea pigs can cool down through their ears too. Get them used to very, very swallow water. Enough to cover their toes. Had a rabbit my dad left out and forgot about so it didn't have shade when the sun moved. We took him to the vet but by the time we got him to it, he was fine.
You can also freeze water and put it in front of a fan. Line windows with tinfoil. Open the windows at night, close them before it gets hot. I lived upstairs with no AC in 100+ weather.
My personal rule of the thumb is that if I'm too cold or too hot, it's too much for any pet.