Hi,
mode with 2K ohm resistor is good, but it is not for long time.
Whole problem with BMW engine HOT Start is faulty electronic in High pressure diesel injection BOSH pump. Mechanically is undestructable, but Electronic part is real problem.
1. symptom is this, HOT Start problem.
2. symptom is this, Engine have bad idle, rpms are going up and down
3. symptom is this, When you drive with specified rpms ( 1500 rpms ), constant pressed accelerator, car cannot drive in constant speed.
This problem can be solved permanetly only when you change electronic part on BOSCH high pressure injection diesel pump.
Sorry for my English, but this is absolutely true. I have Opel Omega with 2,5TDS BMW engine and i have same problem. And now Lande Rover, Range Rover. Same problem and same solution.
This problem cannot be visible on Diagnostics. If everything is good on your car, problem is this Electronic part.
Repair is in Czech Republic very expensive, about 800 pounds.
GL.