In this study, the accuracy of the conventional method that is employed to determine the thermal conductivity of fluids with the transient plane source (TPS) technique is evaluated experimentally using six different fluids. It was found that the accuracy of this method is insufficient for calculating the thermal conductivity of fluids due to: (1) the technique's inability to resolve the volumetric heat capacity in close proximity to the sensor, leading to highly erroneous calculations of thermal conductivity at early time scales, and (2) the lack of any means to predict whether the onset of natural convection will have an effect during testing. As a result, a new method is developed that utilizes the known volumetric heat capacity of a fluid and the equation used to predict the onset of natural convection that was developed in Part I of this study, which is published separately. Results suggest that this new method yields highly accurate calculations for the thermal conductivity of fluids (within 5.6% of values reported in the literature) over a wide range of Prandtl number (Pr = 0.7-11,000) and temperature. (C) 2013 Elsevier Ltd. All rights reserved.