My 85k 330d auto, on a pretty cold morning, can sound really groggy for around 10 seconds and on occasion stalls. If it does stall then the second start is fine after the 10 seconds. It drives fine and makes me think it may need either some redex put through it or a new set of glow rods (dunno when they were last changed). It had a service 5k miles ago.
It's never been a problem, just a minor concern this winter - I realise Diesels can be groggy to start on cold mornings but I just wanted to check other people have had this issue! Again, cold morning after 10 seconds she's fine, warm day she's always fine!