A numerical study is performed to investigate thermal transport phenomena in circular Couette flow in a concentric annulus, in which an axially rotating inner cylinder and stationary outer cylinder are strongly heated under the same heat flux condition. The anisotropic heat-transfer model together with the anisotropic k-ε turbulence model is employed to determine thermal eddy diffusivity. When the inner cylinder is at rest, the turbulent kinetic energy and temperature variance substantially diminish over the whole annular cross-section along the flow, resulting in laminarization, i.e., a deterioration in heat-transfer performance at the inner and outer cylinder walls. In contrast, a substantial reduction in the turbulent kinetic energy and temperature variance in the laminarizing flow is suppressed in the presence of inner core rotation. In other words, inner core rotation contributes to the suppression of laminarization in a strongly heated gas flow. These characteristics in thermal fluid flow with temperature-dependent thermal property are summarized in the form of dimensionless heat flux parameter versus inlet Reynolds number with the Taylor number, as the parameter.