New absolute measurements of the thermal conductivity of liquid n-hexane, n-heptane, and n-decane are reported. The measurements have been carried out in the temperature range 300-370 K at atmospheric pressure in a transient hotwire instrument. The accuracy of the measurements is estimated to be plus or minus 0. 5%. The density dependence of the thermal conductivity of n-hexane and n-heptane is found to be well described by a universal equation for the hydrocarbons based on a rough hard-sphere model. The measurements of the three hydrocarbons studied are also employed to generate more accurate effective core volumes, which are the only parameters characteristic of the fluid required for the application of the proposed universal scheme.