A new phenomenon of turbulent thermal diffusion is discussed. This effect is related to the dynamics of small inertial particles in low-Mach-number compressible turbulent fluid flows. Turbulent thermal diffusion is caused by the correlation between temperature and velocity fluctuations of the surrounding fluid and leads to relatively strong nondiffusive mean flux of inertial particles in regions with mean temperature gradients. It is shown that turbulent thermal diffusion under certain conditions can cause a large-scale instability of spatial distribution of particles. Particles are concentrated in the vicinity of the minimum (or maximum) of the mean temperature of the surrounding fluid depending on the ratio of material particle density to that of the surrounding fluid. At large Reynolds and Peclet numbers the turbulent thermal diffusion is much stronger than the molecular thermal diffusion. Turbulent thermal diffusion can be important in various naturally occurring and industrial multiphase flows. In particular, this effect may cause formation of inhomogeneities in spatial distribution of fuel droplets in internal combustion engines. It is conceivable to suggest that the effect of turbulent thermal diffusion can play an important role in a process of soot formation in flames and in atmospheric dynamics of pollutants, e.g. smog and aerosol clouds formation.