My $0.02 on this...
Use the BC to watch the engine temp. If you can't get above about 75DegC. - the thermostat is shot. A good thermostat will take the engine to 88DegC. and keep it between 88-92DegC.
Yes, you can replace thermostat on an M57TUD30 in a E53 without removing the fan - but NOT on the M57D30 (i.e. you CAN on a facelift/LCI but CAN'T on a pre-facelift).
I drained some of the coolant before pulling the thermostat - it's less messy that way. Drain is on lower left end of radiator. Use a 10mm socket to open it - or is it a 12mm?
UAN - there's no codes in the diesel regarding the thermostat - it's not controlled by the DDE.
And yeah - always use a genuine BMW part for this - unless you enjoy replacing it often.
