The Cobourg limestone is a very low porosity rock consisting of lighter nodular regions that are predominantly calcite and darker regions consisting of calcite, quartz, dolomite, and an appreciable clay fraction. This paper presents the application of the theory of multi-phasic composites to estimate the possible maximum effective thermal conductivity of the heterogeneous rocks. The thermal conductivity estimates are expected to be representative of the intact rock, without fractures or fissures that can influence the heat conduction process. The estimates are therefore indicative of the thermal properties of the rock in undisturbed regions unaffected by the influences of stress relief and excavation damage during construction of deep ground repositories for the disposal of heat-emitting nuclear waste.