Scattering spectra from X-ray, electron or neutron diffraction experiments are sufficient to describe the phase behaviour of noble gas clusters and to determine their temperature. Using classical Monte Carlo simulations combined with optimized data analysis and Path Integral Monte Carlo calculations as ''idealized experiments'' we obtain scattering spectra of Ar- and Ne-clusters. Starting from the classical and quantum mechanical hypervirial theorems we devise a method to estimate the temperature and the caloric curves (which describe the phase behaviour of the noble gas clusters) directly from these scattering spectra using an interatomic potential function as input. As applications we studied for Ar-clusters the effect of different model potentials on the temperature estimate thus contributing to the intricate question of what experimentally is the temperature of an isolated cluster. For Ne-clusters we investigate the differences between classical and quantum mechanical treatment.