If both systems support X Windows, you can set your DISPLAY variable
on your remote machine to your local display and then have emacs run
your local display. I infer from your comment about "other Windows apps"
that your desktop computer is not a UNIX (or Linux) box.
> I think it would be easy enough to use FTP to do the file operations on
> the remote machine, and keep a temporary copy of the file on the local
> machine while doing the editing.
Actually, it's harder than you think. Either your local application has
to implement FTP (nontrivial) or control another application local to
your machine that implements FTP (also nontrivial if you want it to work
crossplatform).
Again it's a matter of determining how we are going to decide on how we
are going to decide what application to attempt. For the basics of what
you want, emacs itself can do most of it.
dsc