I have used MS Live Mesh for synchronization which works similarly to Dropbox.
For synchronization between computers, you do not need to worry about the location of these temporary files created with Ctl-J. That data lives in the *.urd file which is updated when you stop editing the file externally.
The files that are created with the Ctl-J (edit files externally)
http://www.kinook.com/UltraRecall/Ma...externally.htm
a. don't need to be synced because the changes made made in the external app are updated into the *.urd file when the external app is saved or closed.
b. shouldn't be available to be synced because all temporary files created by UR are automatically deleted when UR exits.
c. probably shouldn't be synced...I don't think that you are trying to edit the external material simultaneously on 2 computers...that would seem too risky to me.
So think of the temporary files as just a scratch pad for the real document that is inside the *.urd file.
Hope this helps.