I have a 1990 MB 420SEL. It starts easily but stumbles and backfires when it is cold. As soon as my Temp guage needle reaches the first tick mark it smoothes out and runs well.

I recently replaced the distributor cap and rotor, the fuel pump relay (pump works) and plugs. I used a timing light and noticed that the spark was not occuring steadily. I ordered a new coil. The engine is now running rougher and it quits when I stop.

Is there any way to test the Ignition Control Module (Bosch 0 227 400 693)?

Mine does the same thing when cold (as in under 45-50F outside when started) but to a lesser degree, it runs fine unless you exceed about 40-50% throttle within the first couple minutes of driving, after that its fine.

I suspect it could be a temperature sensor issue or an issue with the fuel distributor...

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This may sound silly but make sure your plug wires sequence was correctly plugged into the distributor cap.

Also make sure you have the correct plugs.
Some types, although categorically appropriate for your w126, may not behave the best. Its been a while for me and a W126, so I can't recite the plug types.

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1979 300D 220 K miles
1995 C280 109 K miles
1992 Cadillac Eldorado Touring Coupe 57K miles SOLD
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1979 240D 140Kmiles (bought for parents) *SOLD.
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1989 300SE 148 K miles *SOLD

Cold starting is aided by the Cold Start Valve (CSV), however when the CSV shuts off, the mixture can be left in a lean condition which may cause backfiring. The leanness can result from: 1) mis-adjustment of the main mixture setting, 2) dirty injection nozzles, 3) improper signal from coolant temperature sensor, 4) delayed signal from the O2 sensor.

Have you tried replacing the new coil with the old? Any change?

There is an outside chance that the ignition trigger pickup at the flywheel is not supplying a good signal when cold, but improves when warm.

There is no convenient field test for the ignition module (EZL).