I have just had the same thing happen to me through a conservatory roof onto a wooden chest. I found a great tip is to place a teatowel on top of the water mark area and iron over the top. Hold the iron still on the affected area for about 5 seconds, remove the tea towel and wipe off the sweat mark. I had to repeat it about 5 times on each area but it removed the marks! It works by drawing the water out with heat. I think it only works on white water marks not black marks as when it is black the water is too deep into the wood. Hope that works for you!
Olly Baldwyn, December 2008