Date registered: Jun 2012
Vehicle: 1998 E320 base sedan @ 160kmiles
Location: Boca Raton, FL
Mentioned: 79 Post(s)
Quoted: 1170 Post(s)
Possibly an aging Crankshaft Position Sensor.
Your car has a Tip-Start feature, meaning you do not have to keep the key in Start key position. After the start request, the ECU monitors the signal that comes from the CPS (aka CKP). When the rpm exceeds certain threshold value, the ECU deems that the car has started (the engine is running), and deactivates the starter relay.
An aging / dirty CPS will cause the signal to the ECU to weaken especially when the engine is hot. In advanced cases,
the car will not start till the engine is cooled down.
There may be other reasons too (related to engine temperature).