Sustainable energy technologies often use fluids with complex properties. As an example, sulfur is a promising fluid for use in thermal energy storage (TES) systems, with highly nonlinear thermophysical properties. The viscosity of liquid-phase sulfur varies by four orders of magnitude due to polymerization of sulfur rings between 400 K and 500 K, followed by depolymerization of long rigid chains, and a decrease in viscosity, as temperature increases. These properties may compromise the accuracy of long-established empirical correlations in the design of TES systems. This work uses computational fluid dynamics to compute steady-state free convection heat transfer coefficients of sulfur in concentric cylinders at temperatures between 400 K and 600 K. The results show that uneven distributions of high and low-viscosity sulfur in the system cause variations in flow patterns and highly nonlinear heat transfer coefficients as temperature gradients increase. As a result, existing empirical correlations for describing system performance become inaccurate. Comparisons of simulation results to predictions from well-established literature correlations show that deviations may surpass 50%. Nusselt versus Rayleigh number correlations for heat transfer are significantly affected by the loss of self-similarity. The analysis proves that existing correlations are not able to capture the complex properties of sulfur in this temperature range, suggesting that alternative modeling techniques are needed for the design and optimization of sulfur TES systems. These challenges are unlikely to be limited to sulfur as a working fluid or TES but will appear in a range of energy systems.