In this paper, we study the plasmonic thermal conductance of ordered stacks of metallic nanorings in a host material. Using second quantized formalism of the Random Phase Approximation, we first determine the dispersion relations of surface plasmon waves on the stacks of nanorings. Then, using Landauer-Buttiker formalism, we determine the coefficient of plasmonic thermal conductance and heat current through the stack as a function of temperature, radius, spacing of rings and dielectric constant of host material. Our results indicate that ordered stacks of metallic nanorings have potential plasmonic thermal properties for heat transfer in nanostructures.