The difficulties of accurately measuring thermal properties, such as thermal conductivity of fractured and/or vuggy rocks are well known. Many commercially available methods are suitable only for liquids or re-packed sands. Others either require samples to be fairly uniform or are potentially destructive due to sample size limitations. In-situ measurements are possible, but can be costly. It can also be affected by in-situ distributions of fluids in the fractures and vugs, such as water, oil and possibly gas. In order to adapt the highly non-uniform nature of the carbonate cores without having to create further destruction of these cores, we developed a non-destructive method for measuring thermal conductivity of highly vuggy and moderately fractured carbonate cores in their whole diameter. In this paper, we report the theoretical background of this methodology; laboratory observations of thermal behaviours; data analysis and resulting thermal conductivity values of carbonates cores. Using this method, we measured 20 cleaned carbonate cores (88 mm in diameter) from Grosmont C and D Formation in Saleski area. Measured thermal conductivity values ranged from 1.00 to 2.87 W/m•K in Grosmont C, and 0.82 to 3.16 W/m•K in Grosmont D. These values were determined to be a strong function of porosity rather than mineralogy, as the Grosmont Formation typically consists of greater than 95% dolomite. These measurements are also shown to be in good agreement with prior studies on non-fractured dolomite reservoirs. A correlation for thermal conductivity was derived which can be used for numerical simulation models.