Keeping fermentation temps below 70

It seems that spring has come early to many parts of the country, especially to the Coast of NC, which is driving fermentation temps higher and higher. I keep my carboys in an interior closet but even then the temps can climb to 70+ when the weather warms. We live on a slab and do not have a basement. Could I keep my carboys in a Tupperware tub partially submerged in water and add ice daily to keep temps lower? If the water temp is say, 68, would that also mean that my wort temp is 68? Any other ideas on keeping temps down? I do not have a designated fridge.

Yes what you're talking about, we call a swamp cooler...Adding a t-shirt over the vessel to wick up the water and help it evaporate will help cool it as will a fan

+1 to what Revvy says. I did the old carboy water bath with a t-shirt method for years. His suggestion of using a fan will help as well. I would usually have a fan set to oscilate back and forth over the keg.