I wouldn't do it on a Hot engine... just think, hot metal, cold water = crack? Not sure, but not something I'd like to find out the hard way
I've cleaned the bay a few times, I've never used degreaser though. My engine really doesn't have a lot of "gunk"... it's just dusty/gritty, so i find water and some selective Simple Green to do just fine.
At home, I just pull the car into it's "bath space", engine on maybe 20 sec, so it's plenty cool. When I have to do a DIY-bay wash, the bay is within 5-10 min from my house, so again not like a 20 min highway drive. I generally save the engine for last, either way, so I'm sure it cools some.
I have a Duratec, so your Zetec looks different. I've never covered up anything either (I could be a terrible role model?) My CAI filter is mostly protected under the fender, and I avoid directly spraying the coils-on-plugs on the valve cover area.
At home, I like to rinse off the bay with a hose, without a nozzle on it... that way you don't get the "collateral spray" all over the place, seems more accurate? I give everything a brief rinse (except the filter/coils) and then get into the nooks and crannies with an old toothbrush, shop/paper towels, rags... whatever I have with me that day. Then I apply some SG to the particularly yucky areas (my valve cover generally looks grody) and scrub that with a rag, and rinse.
At the carwash bay, it's a little more annoying, since there's no spray control. I put the sprayer on regular water (no soap or "engine clean foam" setting - nasty). Then same deal, just try not to drench the questionable parts. A real quick spray though, is probably no worse than driving in a downpour, the engine gets pretty wet in the rain, so I try not to freak too much. Just don't deluge the whole thing, it rarely needs it.