The two cylinders on the top of heater hose sound like the heater core control valves left and right. (if by right side of engine bay you meant left (just in front of the USA left hand drive steering wheel)). I suspect that they get "cooled "from the coolant going through sui they are used to temps over 200 but why so hot when not even being used.

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2011 E70 • N55 (me)
2012 E70 • N63 (wife)