I don't profess to know japanese well, or even at all. Thanks for covering my tracks :) I see how your translation makes more sense - didn't come to me originally though.
I post comments when I think the previous translator might be interested in seeing the correction. :-) In this case, the main thing to remember is that Xしてから means "after doing X", not "because X". It's also worth noting that 冷ます is transitive.