If the problem you're describing is that the car holds 2nd gear longer than normally when the car is very cold, it's designed to do this. Search the archives and you should find more discussion. The W124 300E/TEs have a cold start feature that keeps the engine in the lower gear longer on cold starts to warm up the catalytic converter. This is due to a 60 second after cold start emissions test that they had in Germany, forcing them to figure a way to warm the cats quickly.

There have also been alot of posts about why does my car start in second gear, which is another design feature. On the W124 300E/TE, you only get first gear by flooring the accelerator from a dead stop or placing the shifter into the lowest gear position on a dead stop.

If the tranny is really flaring, this is usually a condition where the engine revs higher in between shifts and is a different problem.

HTH,