I thought the new battery helped alot in mine until I had the starter reworked (we really had to overuse the starter to get the car running after it had been sitting for 3 years), now it really spins. Starts very well until temps are in the teen's and then I have to roll it off the starter.
Valves are next.

You might do a search on this problem, there is a lot of info already on this site.
One thing I read here that seemed to help me was when it is very cold compress the pedal three times and hold it part way down before trying to start.
The other suggestion I see a lot is to cycle the glow plugs a time or two and leave them on an extra 30-45 seconds before trying to start. I don't know how this works since mine is setup differently. (1976 240d)

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Ncnetman
1978 300cd fresh paint
1965 Mustang
1968 Torino GT fastback
2015 VW Passat TDI
1969 Ranchero- project
1974 240d 4-speed -for sale
1976 240d - for sale
1990 6.2 Suburban 194k-getting a 6.5 turbo
2008 Duramax Silverado-totaled
1959 Chev 3100 Fleetside - sold