First thing you should do is try to open one of OneNote's automatic
backups. Go to File->Open Backup, and see if one of the three computers
has a recent backup. You may also be able to change the extension of the
temp file to .one, and OneNote might be able to open it in that case.

To determine what happened I'd need to know a few things about the
network storage:
Are you using Windows Offline Files, or any similar offline caching/sync
tool on the folder in question? If so, I'd recommend disabling them for
your OneNote notebooks, so that OneNote can handle the caching/sync itself.
Also, is the server where the notebooks stored a Windows machine, or
something else? There have been some reports that notebook optimization
might be hitting server errors on some Linux servers, which would
account for the creation of the temp file.

Ilya