We had three Peugeot Diesels (504, 504 wagon and 505 turbo) when I was growing up in Buffalo, N.Y. so I have some experience with getting those running in pretty cold weather. All three of them were slow to get running smoothly in really cold weather. I can't remember them ever failing to start but it took some feathering of the accelerator and sometimes a few tries to get them to begin to smooth out. The 505 was not too bad but both the 504s were pretty cold blooded and needed to be driven a little to really run right in cold weather. By all means check all the items suggested above but don't be surprised if the Peugeot engine never gets as smooth as your Benz. You may have also noticed that the Pug is noiser too, even when warm. The Benz is just a better design I guess.

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LRG
1987 300D Turbo 175K
2006 Toyota Prius, efficent but no soul
1985 300 TDT(130K miles of trouble free motoring)now sold