I can see some missunderstanding happening here. 300E24V is correct in his understanding of the way his car should behave. Like all earlier W124s, it should start in 2nd UNLESS either a lot of throttle is used OR the selector is shifted to "2". In these cases it should start in 1st, cold or hot. The later W124s always started in 1st but had an additional feature where the low gears are held longer when cold to provide faster warming of the catalysts. The early W124s did not do this.
300E24V has a legitimate problem. His car will allow a 1st gear start using the selector when cold but not when hot. He is wondering if anyone knows the cause of this problem.
107.023: 350SLC, 3-speed auto, icon gold, parchment MBtex (sold 2012 after 29 years ownership).
107.026: 500SLC, 4-speed auto, thistle green, green velour.
124.090: 300TE, 4-speed auto, arctic white, cream-beige MBtex.
201.028: 190E 2.3 Sportline, 5-speed manual, arctic white, blue leather.
201.028: 190E 2.3, 4-speed auto, blue-black, grey MBtex.
201.034: 190E 2.3-16, 5-speed manual, blue-black, black leather.