Hey MarkT,
just a note to say thanks for the help!
Using you advice and the code as a starting point, I managed to put something together which works quite nice. It still has some issues at some break points where it is several % off in the reading. Haven't tracked it down yet, but I am convinced it is down to the way I round off the temperature and do look-ups to finally interpolate a value, using a table from the EFS-10 data sheet.
If you are interested, I have documented the result here, including the code. GitHub - aweijnitz/Hygrometer: Basic Arduino sketch to measure relative humidity and temperature using an EFS-10 and an LM135.
Thanks again!
Anders