  We propose a novel component to the understanding of the temperature
structure of galaxy clusters which does not rely on any heating or cooling
mechanism. The new ingredient is the use of non-extensive thermo-statistics
which is based on the natural generalization of entropy for systems with
long-range interactions. Such interactions include gravity and attraction or
repulsion due to charges. We explain that there is growing theoretical
indications for the need of this generalization for large cosmological
structures. The observed pseudo temperature is generally different from the
true thermodynamic temperature, and we clarify the connection between the two.
We explain that this distinction is most important in the central part of the
cluster where the density profile is most shallow. We show that the observed
pseudo temperature may differ up to a factor 2/5 from the true thermodynamic
temperature, either larger or smaller. In general the M-T and L-T relations
will be affected, and the central DM slope derived through hydrostatic
equilibrium may be either more shallow or steeper. We show how the true
temperature can be extracted correctly either from the spectrum or from the
shape of the Doppler broadening of spectral lines.
