These symptoms sound very much like what just happened with my 2000 C280 where there is a failure with either the camshaft position sensor or crankshaft position sensor. It starts with an non start after having driven sometimes a short distance, sometimes a longer distance. Then it spread to the first start of the day and then progressed to the car shutting down while coming to a stop. It happened during a hot spell and it did seem to be heat related. Simply waiting awhile and it would restart. First I tried replacing the front camshaft sensor but it turned out to be the rear crankshaft sensor.

glenmore
1991 300CE
2000 C280
1990 LS400