You have the right idea. A hot grill is much easier to clean than a cold one. I just turn to high, wait a few minutes unil the temp gets in the 500 range and then use your grill brush to scrape off all food particles, sauce, etc.
If by some chance you forget to clean. Just fire it up next time you cook. Let it burn for 10-15 minutes, then clean, lubricate, and cook.