Any time I wanted to clean up my cooking grates I used Dawn, and give 'em a soak for 30 minutes or so before hand-washing. Don't use abrasive cleaners or pads...that will eventually wipe the chrome finish right off of them. If they're really grungy they may need a longer soak and hotter water.
Anymore though, I let the residue build up...helps protect the grates once you have a good petina built up...a little exposure to higher heat (~400*F) will help to develop it more after each smoke, then just bust of the bigger drippings with a metallic brush while heating up the smoker. If you want a clean smoking surface for items such as cheese try aluminum disposable grill toppers...you can reuse them with a little cleaning, too, and being they are not a composite material you get more aggressive with cleaning methods and not hurt them, barring strong acids/caustics, of course.
BTW, excessive heat could damage the finish, or if not heated evenly may cause the thinner wire grates to warp.
Eric