Embodiments of the invention are directed to bearing assemblies configured to effectively provide heat distribution from and/or heat dissipation for bearing element, bearing apparatuses including such bearing assemblies, and methods of operating such bearing assemblies and apparatuses. In an embodiment, a bearing assembly includes a plurality of superhard bearing elements distributed about an axis. Each superhard bearing element of the plurality of superhard bearing elements has a superhard material including a superhard surface. Additionally, a support ring structure that includes a support ring that supports the plurality of superhard bearing elements and a thermally-conductive structure in thermal communication with the superhard table of each of the plurality of superhard bearing elements. The thermally-conductive structure has a higher thermal conductivity than the support ring of the support ring structure.