It wasn't that damp at all. Probably because "the cottage" is rather large, it actually has a dedicated a/c unit for each floor. It was the upper floor, with the bedrooms, that had the a/c failure. By running the a/c unit on the main floor constantly, that kept the air relatively dry on that level. As the air warms on the first floor, it rises in the center staircase, much like a chimney, so it dries out even more.
But 90 degrees - which is what it reached upstairs yesterday before they did the temporary fix (and was the reason I wasn't here - I turned off the computers to prevent them from overheating) - is pretty darn uncomfortable, humid air or no.