Yes it will, because in Mercedes benz the heater core is kept cold by stopping the coolant at the control valve, the system adds heat as required to warm up the core to the desired set temperature of the control panel.

If the valve fails open the core is now fully hot - and will overpower the A/C system.

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2012 BMW X5 (Beef + Granite suspension model)

1995 E300D - The original humming machine (consumed by Flood 2017)
2000 E320 - The evolution (consumed by flood 2017)