The luminosity of X-ray pulsars powered by accretion on to magnetized neutron stars covers a wide range over a few orders of magnitude. The brightest X-ray pulsars recently discovered as pulsating ultraluminous X-ray sources reach accretion luminosity above $10^{40}\, {\rm erg\ \rm s^{-1}}$ which exceeds the Eddington value more than by a factor of 10. Most of the energy is released within small regions in the vicinity of magnetic poles of accreting neutron star - in accretion columns. Because of the extreme energy release within small volume accretion columns of bright X-ray pulsars are one of the hottest places in the Universe, where the internal temperature can exceed 100 keV. Under these conditions, the processes of creation and annihilation of electron-positron pairs can be influential but have been largely neglected in theoretical models of accretion columns. In this Letter, we investigate properties of a gas of electron - positron pairs under physical conditions typical for accretion columns. We argue that the process of pair creation can crucially influence both the dynamics of the accretion process and internal structure of accretion column limiting its internal temperature, dropping the local Eddington flux and increasing the gas pressure.