I have a termistor that I would like to connect to Arduino board get the temperature to later control the electric waterpump in my sportscar.
However I am a newbie to electronic design, but I understand that I need to have a resistor connected and based on the spec sheet below but should the resistor value be 100 kOhm or something else?
It seems that examples/tutorials have the same value of resistor and termistor (at 25 degree celsius), e.g. Arduino Thermistor Tutorial
This is one of those problems where you pull out a spreadsheet program, stick in the values, and then test what your analogReading will be given various resistors used in the resistor divider. I'd highly encourage it at least once so you can get a feel for how things work.
But getting right to the point, if you want to be monitoring your engine for (e.g.) 90C, or that's where you want the most precision in your readings, then you would use a resistor equal to the resistance of the thermistor at that temperature (~9K).
At 90C: 5V * (9K / (9.156K + 9K)) = 2.48V -- analogRead around 507.
At 95C: 5V * (9K / (7.662K + 9K)) = 2.7V -- analogRead around 553.
The difference there (553 - 507) is 46 for a 5C increment, but around 20C:
At 20C: 5V * (9K / (124.9K + 9K)) = .33V -- analogRead around 67
At 25C: 5V * (9K / (100.0K + 9K)) = .41V -- analogRead around 83
83 - 67 = 16. Not as much precision for that 5C increment.
Thanks for a very good explanation 
I will start with a 10K since I have that and do some tests and logging of values.