To kill the leftover processes and clean up the temporary files created, put this in a text file:
Save this script as "raysource.sh" (or something like that), and in Terminal, mark it as executable by running this:
cd ~/".wine/drive_c/users/$name/Local Settings/"
mv "Temporary Internet Files" "Temporary Internet Files-bak"
mkdir -p "Temporary Internet Files"
killall -w peer.exe PeerAdaptor.exe
rm -rf "Temporary Internet Files"
mv "Temporary Internet Files-bak" "Temporary Internet Files"
Now any time you want to run RaySource, just run this script instead. It'll run raysource.exe, then when you close the program, it'll kill those two pesky processes, then it'll remove all the files in "Temporary Internet Files" that were created by RaySource, while leaving any temporary files created before by other programs intact. Replace "your name" with your name (the name under ".wine/drive_c/users/"), and replace the path with the actual path to the executable (e.g. "/home/user_name/cool stuff/raysource.exe").
chmod a+x raysource.sh
This is just one solution. Other people might have other ideas.