  Theoretical studies of the physical processes guiding the formation and
evolution of galaxies and galaxy clusters in the X-ray are mainly based on the
results of numerical hydrodynamical N-body simulations, which in turn are often
directly compared to X-ray observations. Although trivial in principle, these
comparisons are not always simple. We demonstrate that the projected
spectroscopic temperature of thermally complex clusters obtained from X-ray
observations is always lower than the emission-weighed temperature, which is
widely used in the analysis of numerical simulations. We show that this
temperature bias is mainly related to the fact that the emission-weighted
temperature does not reflect the actual spectral properties of the observed
source. This has important implications for the study of thermal structures in
clusters, especially when strong temperature gradients, like shock fronts, are
present. Because of this bias, in real observations shock fronts appear much
weaker than what is predicted by emission-weighted temperature maps, and may
even not be detected. This may explain why, although numerical simulations
predict that shock fronts are a quite common feature in clusters of galaxies,
to date there are very few observations of objects in which they are clearly
seen. To fix this problem we propose a new formula, the spectroscopic-like
temperature function, and show that, for temperature larger than 3 keV, it
approximates the spectroscopic temperature better than few per cent, making
simulations more directly comparable to observations.
