The worst way to plumb an icemaker?

We were told by the previous owner that the icemaker in the fridge didn't work because there wasn't any plumbing running to it. When the refrigerator was replaced, we found that there was, in fact, a copper line running to the icemaker, but it was crushed, as the refrigerator had rolled over it. I asked A. to buy a new line for it, which turned out to be about 8" too short. When I was able to extend the line, I found that the pipe it connected to was warm to the touch - not something that you want with an icemaker, but one that caused my parents trouble with their icemaker for years.

I looked at the pipe, but it wasn't connected obviously to the hot water heater, so I set this problem aside to deal with another day, after I'd had time to think about it. This time, the line was hot to the touch. I traced the pipe to the extent that I was able to - and found that it ran into the boiler! Eeew.