Okay, here's more info about the problem:
The good news is that it apparently goes away after a while (it took a few hours). Perhaps some very large file is being downloaded and is hogging a substantial fraction of the wifi bandwidth. Don't know what file -- I had turned off all the backup, iCloud, and wifi sync controls that I could find. Some of the other posts are complaining about forced automatic download of IOS updates, so it may be that.
Interestingly, I later brought the phone to the Apple Store with another problem, and they had to wipe and reload the firmware and IOS. This caused the problem to return. As before, I left it plugged in for several hours and the problem went away.
Don't know if or how often this might recur, but at least for now it's not causing problems.