Heat and a brush will work just fine..
BUT why bother? Buy new screws, esp on a set of rings you have used or bought used. They streach and with the fine thread really are not made to work over and over. BEST part they are cheap! A trip to most GS will net you the needed screws. IF none close enough Midway and Brownells will ship them out quickly.
One last point, Personally I never lock tight rings, only bases. Ring screws can be easily and quickly checked unlike bases that are under the scope.
CW