The increasing imperative to reliably forecast thermal recovery in bituminous reservoirs has heightened interest to study thermal properties of rock-fluid systems, notably that of thermal conductivity. Several measurement techniques have been developed. However, these are typically fraught with limitations aiming at an amenable analytical asssessment. As a result, complex calibrations are implemented, which are susceptible to numerous errors. In this paper, an alternative, more accurate and unique method of thermal conductivity measurement is presented. The method combines two different measurement systems that are capable of measuring heat flux axially and radially. Nonetheless, in both experimental systems, heat is transferred across the test sample after a temperature gradient is established between two defined regions of the sample. The apparati are complemented by computational fluid dynamic models that mimic the physical models at the measurement conditions. A combination of the physical measurements and numerical simulations under steady state conditions is used to provide the final thermal conductivity values. A number of fluid and reservoir samples are tested in order to demonstrate the capabilities of the method. These tests provide evidence of the utility of the method in allowing for variability of sample form, as well as temperature and pressure conditions. Furthermore, both physical experiments and computational models permit and sufficiently account for fluid flow while thermal conductivity is being measured. It is shown that this method is distinctively able to yield accurate results irrespective of the sample size and shape limitations, and attendant heat losses.