Hi MerryRecluse.
Yeah, the sweating is completely normal during withdrawals / initial sobriety. Your liver controls your body temperature, and it's a little out of whack right now.
As for how long it lasts, it differs from person to person. For myself, it's generally about 5 days, and I'll begin seeing a noticeable difference, then it continues to dissipate after that. Not sure how true this is, but I've heard forced sweating (ie. sauna) can help speed up the process to get rid of the sweats. I do it myself, but that's because it's easy for me -- my entire yard is a sauna, so I just sit outside with a cup of tea.