Some folks don't realize those things actually get hot. I guess it isn't intuitive because it came as a surprise to me. To give you some idea, just two days ago I was helping my neighbor spread some asphalt for a new driveway. We had a lot of trouble because it melted and was sticking to everything, the tires on my tractor were covered with about an inch of the stuff. We finally gave up and waited until the next morning. During this process one of the pins from the scraper blade on the tractor fell off and I had to find it. When I picked it up, it burned my hand and I just popped the blister it raised on my left index finger. High temperature today, 116F, but it's expected to be cooler tomorrow, around 113F. By 0900 it was over 100F. However, you do get used to it, I keep my swimming pool at 94F during the summer so I don't freeze when I get in it.
So, you can see why something that gets hot on its own isn't something that we want to put in a closed metal box outside. Good old contactors. In your neck of the woods though, it could have worked fine, even as suggested, mounted to the hot water heater.
But, I don't get much snow, and the girls don't wear much.