The changes in character of deformations in thin indium layers as a function of temperature and directions in crystals during rigid low-temperature thermomechanical cycling in the range of 2–300 K are investigated. As determined, the growth of anisotropy in thermal-elastic deformations brings about ‘negative’ dilations in some crystallographic directions under the stress $\sim {\sigma_B}$ in the range of 15–(80)100 K. It occurs at the process of transition from isotropic polycrystalline contacts to quasi-anisotropic 2D-nanocontacts in this metal. Within the framework of a dislocation model, the mechanisms of accumulation of such level of mechanical tension under conditions of limited space and minimal mobility of dislocations are analyzed in indium layers. The height values of Peierls barriers for kinks at dislocations and the coefficients of their transparency in indium are estimated as well. High probability of overcoming the barriers arises when kinks solitons penetrate them (tunnelling) in such crystallographic directions for which Poisson’s ratios $\nu \sim$0.5. These directions can serve as relaxation channels for destructive stresses accumulated in the layer.