While fish can sometimes live at higher temperatures, most corals would likely die.
I live in Arizona and during the Summer its 105 degrees outside and 95 inside (no air conditioning =0). I too was pretty upset at the prospect of buying a 400 dollar chiller but it was well worth the money.
If you absolutely need a cooling system and can't afford a chiller, perhaps try one of those DIY chillers. My friend made a chiller for his aquarium out of a 50 dollar mini fridge drilled to fit a bunch of coiled up tubing. Its not the best and doesn't look too great but it got the job done.
Hope this helps,
Mike15.