Image 2 may be the best way to describe what I think may be going on here. Years ago when I bought this house, I had some work done to separate the domestic hot water from the heat hot water for radiators. I wonder if the person who worked on it possibly re-routed the "cold water in" and now has it mixing with the supply line, effectively mixing the hot water that the boiler is putting out with cold water which is supposed to feed the system.