As talleymonster mentioned, your fermenting wort is going to be warmer than ambient temps because fermentation generates heat. If your basement gets up to 72 degrees, then your wort could easily be in the mid-70's.
Fermenting above the temperature range of your yeast can often produce off flavors, fusel alcohols, etc. Depending on the particular yeast, this may or may not be too significant - but if you can do anything to keep the temp down, it's probably worth doing.
Sticking it in a tub of water is a good plan, and many people will recommend throwing a wet towel over it as well to cool it a bit more with evaporative cooling.