  The origin of the recently reported systematic bias in the spectroscopic
temperature of galaxy clusters is investigated using cosmological
hydrodynamical simulations. We find that the local inhomogeneities of the gas
temperature and density, after corrected for the global radial profiles, have
nearly a universal distribution that resembles the log-normal function. Based
on this log-normal approximation for the fluctuations in the intra-cluster
medium, we develop an analytical model that explains the bias in the
spectroscopic temperature discovered recently. We conclude that the multi-phase
nature of the intra-cluster medium not only from the radial profiles but also
from the local inhomogeneities plays an essential role in producing the
systematic bias.
