Then don't copy it to the desktop?
Caffeine does not require installation, just copy it to a location where your user has write access and run it from there. Nothing more is necessary (for Caffeine to do its job, I mean).
Who is still using that method of doing things on the desktop? Next time you tell me that you use the trashcan to "store" and "retrieve" files too.
My dual monitor setup has only the trashcan icon on it, so you could call me prejudiced...
Besides all of the above, if your user account on the remote computer is so limited in what it is allowed to do, why would you even want to keep the remote connection open for longer than the allotted time?