starting problems only when hot

Bmw E46 318Ci sport convertible on a 03 plate

Car starts first time and runs fine when cold. E.G when its been left all night it will start first time every time.

I covered over 150+ miles with out a problem on the day I bought the car.
But when I stopped off for a cuppa at my sisters house was there maybe 15-20 mins the car would not start and the engine management light was on. the engine turned over and i could hear the fuel pump prime but it did not fire up and the odd time it did it dies.

After numerous attempts it fired up and was like nothing had happened it ran perfect the revs were fine no misfire.

next morning took the car out for a spin with the eml on the car never missed a beat. Plugged it into a code reader and got P0171 system too lean (bank 1) I reset the code and the light has stayed off since (5 Days now).

Been out in the car a few times now and it starts first time every time when its cold of when its had longer then 30mins to cool down. I have had the car to a local company with stealer level gear and the car would not fault also no pending fault

I drove the car home and left it for 15mins then tried to start it It turned over but would not fire up when it did it died after a few seconds plugged in my code reader and got
P1341 Multiple cylinder misfire with fuel cut off
P1343 Misfire cylinder 1 with fuel cut off
P1349 Misfire cylinder 4 with fuel cut off

I cleared the codes and tried to start the car still would not start. left it for 30+ mins and it fired straight up I plug in the code reader and no faults found.

I have changed the temp sensor
and the camshaft sensor (1 at a time)
also cleaned the maf sensor
did a bit of a leak test with some solvent clean around the hoses but the idle speed did not change.

Im a bit confused where to go next since the car runs mint all the time and only has the problem when starting from warm and once its started shows not fault codes at all and the light has not come back even when it fails to start

Any info or help would be much appreciated

Try using some starting fluid (ether) next time it happens. It may be your fuel pump or maybe even a "vapor lock" type problem.

sounds like crank sensor to me.