A simple divided-bar apparatus for studying the thermal conductivity of rocks and soils at permafrost temperatures is described. The apparatus is intended also for use with permafrost specimens tested in their natural frozen state. It has been designed for low heat fluxes and consequent small temperature drops across the test specimen, while retaining a high precision of measurement.Different thicknesses of two water-saturated sandstones and a limestone have been tested as a function of changes in temperature, frozen and unfrozen. Significant corrections for the contact resistance between the specimen and divided bar were determined. The influence of the magnitude of temperature gradient across the specimen was not found to be important for the low gradients employed in these experiments.The measured thermal conductivities show a slight decrease in value with temperature increasing to 0 °C. In the neighbourhood of 0 °C, a sharp reduction in thermal conductivity was observed as the ice–water phase change occurred. It is clear that the magnitude of the thermal conductivity of the rocks depends on their mineral content; quartz, with its high thermal conductivity, plays the predominant role where it is present.