High-latitude permafrost, including hydrate-bearing frozen ground, changes its properties in response to natural climate change and to impacts from petroleum production. Of special interest is the behavior of thermal conductivity, one of the key parameters that control the thermal processes in permafrost containing gas hydrate accumulations. Thermal conductivity variations under pressure and temperature changes were studied in the laboratory through physical modeling using sand sampled from gas-bearing permafrost of the Yamal Peninsula (northern West Siberia, Russia). When gas pressure drops to below equilibrium at a constant negative temperature (about −6 °C), the thermal conductivity of the samples first becomes a few percent to 10% lower as a result of cracking and then increases as pore gas hydrate dissociates and converts to water and then to ice. The range of thermal conductivity variations has several controls: pore gas pressure, hydrate saturation, rate of hydrate dissociation, and amount of additionally formed pore ice. In general, hydrate dissociation can cause up to 20% thermal conductivity decrease in frozen hydrate-bearing sand. As the samples are heated to positive temperatures, their thermal conductivity decreases by a magnitude depending on residual contents of pore gas hydrate and ice: the decrease reaches ~30% at 20–40% hydrate saturation. The thermal conductivity decrease in hydrate-free saline frozen sand is proportional to the salinity and can become ~40% lower at a salinity of 0.14%. The behavior of thermal conductivity in frozen hydrate-bearing sediments under a pressure drop below the equilibrium and a temperature increase to above 0 °C is explained in a model of pore space changes based on the experimental results.