Warmas,
What is it you don't understand about the explanation in that link?
Ignoring the science behind what is happening with the fuel level sender, if you are replacing the thermistor, the one you select needs to match the characteristics of the one that got destroyed. There are no thermistors off the shelf that meet BMW specs. You selected one that is 500 Ohms @25°C. This is too low of a value and it needs to be a 600 Ohm thermistor. The closest ones readily available are 560 Ohms or 680 Ohms. Your best bet is to use a 560 Ohm one and add a series resistor of 40 Ohms. That way, the fuel level sender circuit still thinks it's driving current into a 600 Ohm load. If you keep your 500 Ohm thermistor, then add a series 100 Ohm resistor.