An approximate analysis is made of the heat flow associated with the use of the thermal comparator for the measurement of thermal conductivity. Consideration of the heat flow through the solid-solid constriction does not give a cooling rate proportional to the square root of the thermal conductivity as found experimentally, which suggests that allowance should also be made for the heat transferred through the surrounding gas.The analysis shows that the thermal-comparator method can give information about the effective area of contact and its dependence on load. A proposal is made for a new method of determining the thermal conductivities of powders and for a modified form for the thermal comparator which would be direct reading and more suitable for measurements made in rapid sequence or at high temperatures.