Have you checked that the hub cones are tight? Do this by grabbing the rim and trying to move it side to side relative to the frame. Try this from several places on the rim. If you haven't done so recently, remove the wheels from the frame and feel the bearings for smoothness by turning the axle between your thumb and forefinger. Feel the spoke tension in your wheels. Grab two adjacent spokes that cross each other and squeeze them together. You should be able to move the crossing point by a couple millimeters, but not much more. Feel every pair of spokes. Sometimes there is one or more much looser than the others, usually due to a flat spot in the rim.
If you don't find anything wrong here, I'd be suspicious that the dust cap which surrounds the hub cones has too tight a clearance, so that when it gets hot the dust cap is rubbing the cones. And being wet lubricates it enough to suppress the sound. Interesting problem. I hope you find your solution.
Oil is good, grease is better.
2007 Peter Mooney w/S&S couplers/Terry Butterfly
1993 Bridgestone MB-3/Avocet O2 Air 40W
1980 Columbus Frame with 1970 Campy parts
1954 Raleigh 3-speed/Brooks B72