I would say the revving up to 2k rpms is a bigger issue than having it start off around 1,000 rpms.

The commanded RPM on start up does depend on coolant temp, even with its super cold its still going to want to be at around 1200 rpms.

Have you done anything lately to the car, like a tune up?

Maybe try getting some new spark plugs, new fuel filter, clean the throttle body and MAF sensor really well, all those could help this problem.