Yeah I do think temperature pays a big part. I didn't hear a thing this morning.
The timing chains can be a weak point on the OM651, I think the stop start system causes stress to the chain but the tensioners can also be an issue, mine got noisy at around 90K. I have no idea why Merc decided to run gears for most of the engine components but decided to use a bicycle chain to run the essential Cam shafts at the top of the engine.
Modern engines use chains but most manufacturers make the chains our of extra thin chocolate based steel. Its awful. I have some friends who work in the car trade and they complain about them a lot. I know Nissan and JLR (ingenium engine) have real trouble with timing chains. Maybe if they made them to be more robust it wouldnt be a problem.
Hopefully yours is just a tensioner, I know Merc did revise it, so if you change it get a genuine one and not aftermarket.