Hi,
I’ve recently faced a very strange problem with my 2004 E500 W211 (stock).

I was out for dinner and upon my return (after almost 1.5 hrs) I turned the key after waiting 5-8 seconds at key position 2, before cranking (habit to let the car get fuel pressure and all electronics cycle over)

the engine turned over as long as it could but the car failed to start. Puzzled I tried it 3 more times repeating the same standard procedure. No luck. I checked the dash display for any malfunctions - none. Battery Voltage was 12.0V.
I noticed the ambient temperature reading was at 40 Celsius. Odd since the temp outside would be 32-34C at most.
The water temp was 2 bars below 80.

I went over to the front of the car and noticed the grille was hot. But not enough to be alarmed. I popped open the hood looked around everything seemed alright. No coolant leaks or anything as such out of the ordinary.

I left the hood open and waited 5 mins.

I noticed the ambient temperature reading slowly went down till 35C.
I turned the key and the car fired up and had a check engine light.

I drove home. Stopped to fill gas on the way. The car started without any problem at the gas station.
The ambient temp reading was consistent around 34C throughout. The check engine light was still on.

the next morning I started the car and it fired up without any problems.
After a few turns of the key and a few short start stops to move the car around the check engine light went away it self.

Today, I got back after a day trip with almost 300km. Engine temp remained steady 1 bar over 80.

I parked the car in for the night. After the car was parked for more than an hour. I went to get some stuff out of the car and noticed the ambient temperature reading was at 40C again. The actual temp outside was 32-34 C. Coolant temp was 1 bar below 80.
I tried started the car and it failed to start.
I opened the hood left it for 15 mins and went back to check the ambient temp had gone down to 37C. I turned the key and it fired up on the first attempt with the check engine light on.

I haven’t been able to get the car checked for fault codes since I’m out of my home town.

Does anyone have any thoughts on what is causing this?

 

Read codes (you knew that). Advance Auto, Pep Boys, etc. can do this for you.

Replace the battery if it's one day older than 4 years. Replace the aux battery or voltage converter if this car has one.

Consider that the crank position sensor may be on its way out. This can result in crank/no start.

Otherwise I would look at the fuel rail pressure.

 

Adding to @chassis check list is the fuel level.

Is it above 1/2 level? If not check the fuel level using a scanner since all the fuel may be on the "wrong side pool" of the tank. Seen a nearly half full tank with half the fuel on the driver side only. Once filled above half. The car started immediately.
the fuel pressure test will fail of course, the faulty part is the driver side "pump filter"

 

So I read the codes and it showed L5 sensor (CPS) with code P0335.

I’ve swapped out the sensor and hopefully it should resolve the issue.