You aren't supposed to wash your engine according to the carwash owners around here, unless you have the proper recovery equipment to collect all that grease and oil :roll: . I just go at night. I don't really let my engines get that dirty and I don't let oil leaks linger for too long, so I'm basically just washing off dust and mud.
I do it with the engine running, but I let it cool down before I spray it with the water. Gunk makes another cleaner called Foamy Engine Brite, it works great. I spray everything down and let it sit while the engine cools and the cleaner has time to work. Maybe spend a few minutes washing the undercarriage or cleaning the wheels off while I wait. Then I just crank it back up and spray it off, trying not to concentrate the spray on anything electrical or around the air filter.