Temperature gradient metamorphism is one of the dominant processes changing the structure of natural dry snow. The structure of snow regulates the thermal and mechanical properties. Physical models and numerical simulations of the evolution of the snow cover require a thorough understanding of the interplay between structure and physical properties. The structure of snow and the heat conductivity were measured simultaneously without disturbance in a miniature snow breeder. The structure was measured by microtomography, and heat conductivity by measuring heat fluxes and temperatures. A temperature gradient from 25 to 100 K m⁻¹ was applied to the snow. The snow density range of the samples varied from 150 to 500 kg m⁻³. The density in the observed volume remained constant during the experiments under temperature gradient conditions. The structure was analysed with respect to the size of typical ice structures and air pores, specific surface area, curvature and anisotropy of the ice matrix. The temporal changes in structure and heat conductivity are compared. The heat conductivity changed by as much as twice its initial value, caused by changes in structure and texture, but not due to changes in density. This shows the enormous importance of structure in the evolution of the heat conductivity. The observed changes are not in good agreement with the current understanding of the metamorphic process, because heat conductivity increased during temperature gradient metamorphism, instead of the expected decrease due to a shrinking of the bonds. We also observed a plateau in the evolution of the heat conductivity coefficient, which indicates a quasi‐steady state of the structural evolution with respect to thermophysical properties of snow.