We investigate the influence of a shallow trench on the local distribution of temperature and the ice content in the Martian regolith. The model used in this paper is an extension of that presented in Kossacki et al. (Icarus 144 (2000) 463–478) which was used to analyse heat diffusion and to calculate the temperature distribution in the vicinity of a small surface trench. In addition, our model now includes water vapour diffusion through the pores of the ground regolith, water adsorbtion on the mineral grains and time evolution of the water ice in the regolith. Our simulations predict the diurnal cycle of frost formation within the trench. The subsurface ice follows the topography of the trench and it tends to stabilize the temperature near the trench bottom.