This paper deals with the modelling of the medium pressure Hg and Hg-Ar positive column (Hg pressure range 5-350 Torr). The aim of this work is to simulate, in a first approximation, the middle phase of the Hg high-pressure lamp warm-up. In this approach, the main assumption is that time evolution of the discharge can be divided into a succession of stationary sub-phases characterized by the Hg partial pressure. Thus, we present here a self-consistent steady-state collisional-radiative model describing the middle sub-phase. This model includes volume recombination of Hg atomic and molecular ions, as well as several atom-atom inelastic scattering mechanisms. Calculations are carried out for both pure Hg and Hg-Ar discharges. Our results, which are in good agreement with experimental data from the literature, confirm that plasma thermalization occurs in the middle start-up phase (electron and gas temperatures become equal during this phase). Furthermore, this simulation shows the importance of different elementary processes, like atom-atom inelastic scattering, for the medium pressure plasma description. In fact, these mechanisms cannot be neglected until LTE conditions are reached.