This is a little different than most of the posts that I've seen about this issue. Mine doesn't start, then stall. It takes about 5-6 seconds of cranking to get it to start at all.
So, it has been unusually cold here in Austin, Tx, like down near freezing. I know that's warm for some of you folks right now. The last few mornings, when its cold, the car starts right up, like within a second or so. But when warmed up, it will go back to taking a few seconds to get it going.
I read somewhere that the Coolant Temp Sensor may be responsible. But the radiator fans seem to be working as when it was in the 70's, the car never got above half on the gauge, which also seems to be working correctly.

Do all these things, DME, fans and gauge use the same sensor? or does the r53 have 2 sensors, one for DME and one for fans and gauge? Some cars have two, some don't.

 

I'm pretty sure there's just one coolant temp sensor. I remember looking into that a long time ago, because I had pressed and held the odometer reset button while turning on the key, so that I could get the temp display in numbes (forget which menu option now (maybe #7, or 7.1 ??) but I think it's in the sticky here,.. Same thread as the magical reset). I just wanted to read the exact degrees as the car warmed to ensure my fan would come on correctly after I had replaced a fan lo speed relay.

Anywho, the dme is what triggers the rad fan. I too remember cars that had a thermostatic-relay that screwed into a threaded hole in the rad. R53 are not that way, the DME reads the temp from the one sensor (I wana say it's on the head on the flywheel end of engine, but can't remember) and triggers the fan hi/lo/off according to it's program. DME sends the same signal to the dash guage. I believe DME also reads two other temps, one in the throttle body for intake air temp, and another in the bumper cover for ambient air temp.