Mercedes ML rough running and check engine light

Sounds familiar. I had a similar problem with my old Volvo, although it was a different sensor. The intake air temperature sensor basically tells the car's computer, the ECU, how hot the air entering the engine is. The ECU uses this information to adjust the fuel mixture. If the sensor is faulty, the ECU gets bad data, messes up the fuel mixture, and can cause reduced power, rough running, and trigger the check engine light. Did the diagnostic tool give you a specific error code?

Yeah, the diagnostic tool showed error code P0113, which my limited googling tells me is 'Intake Air Temperature Sensor 1 Circuit High Input'. So, if the sensor is sending wrong information, is it likely that replacing the intake air temperature sensor fixes the problem?

P0113 is pretty much a dead giveaway for a faulty intake air temperature sensor or a problem with its wiring. I'd say replacing the sensor is a very good starting point. Given the symptoms and the error code, it's the most probable cause. However, without seeing the car, it is hard to say for sure. You might want to take it to a trusted workshop.

Thanks a bunch for the help! I took it to my local workshop, and you were spot on. They confirmed the intake air temperature sensor was defective. The repair including the new sensor and labor was around 155€. The car runs perfectly now. Seriously appreciate your advice!