Summarize:

Never cool it with cold water because you could crack the grill rack. Take the grill rack into the kitchen and wash it with very mild soap and water. Too much soap will strip the seasoning, but you do want to clean oils out so they don't get rancid. Avoid soaking your grill rack in soapy water because you'll strip away the seasoning. Rinse thoroughly. Either dry your grill rack with a paper towel or place it in a warm oven for a few minutes. Doing this will allow it to dry out completely between all the joints.
Let your grill cool down naturally after you're done with the day's grilling. Clean it after it has cooled down.