There are probably a few solutions to this.
1. Hide/Disable access to local drives, so they can't store items on the server and then allow Drive Mapping. When they save, instruct them to browse to their desktop via the mapped drive.
2. Roaming Profile. Although I don't like using these too much as they can become corrupt or bloated.
3. Terminal Server Home Drive where they can store files.
4. File Redirection, but I personally haven't looked into this and may/may not work in your situation.