My daughter with CF was a night sweater (not wool or polyester) as an infant. During winter we'd have to put her in non-fleece footed pajamas and the bed would still be soaked in the AM from her sweat.
She has somewhat grown out of it, but there are times when she sleeps really hard (she's now almost 3) that her pillow and/or head of her bed is covered with sweat in the morning.
On a personal note, this is aggravating to me as we do baths at night and in the morning it sometimes seems like we didn't bathe her at all because of how much she sweated. It is CrAzy!!! <img src="i/expressions/face-icon-small-smile.gif" border="0">
I hope that you can figure out why your little one is sweating so much! For us, we were told it was because of her CF and that her sweat would even taste EXCESSIVELY salty.