[derriz]

Temperament is unrelated/orthogonal to inharmonicity. Temperament deals with picking frequencies for the notes that make up the scale within an octave.

Inharmonicity affects how you tune the octaves themselves. The reason a simple doubling rule doesn't work is a result of the properties of real physical strings which are not perfectly elastic causing the harmonics of a single string vibrating to be slightly sharp. To avoid "beating", the ratio of frequencies between two piano notes an octave apart needs to be slightly greater than 2.

This article is half of what a "what every musician should know about piano tuning" article should contain - it's the "set-up" part where you derive a nice simple rule that is widely known. The second part would then deal with temperament (first) and then inharmonicity.