Motivated by the difficulties encountered by engineers to cool down the rotating shafts of industrial machines, the present work investigates the heat and mass transfers in the rotor-stator gap of a Taylor–Couette system with an axial water flow characterized by an aspect ratio Γ = 50 and a radius ratio η = 8/9. Extensive velocity and temperature measurements have been performed on an experimental set-up for a wide range of the flow parameters: the axial Reynolds number Re and the Taylor number Ta reach the values 1.12 × 104 and 7.9 × 107 respectively. In particular, coherent structures close to the rotating wall were measured by Stereo Particle Image Velocimetry. A correlation for the Nusselt number Nu on the rotating wall is finally provided against the axial Reynolds, Taylor and Prandtl numbers. Nu is proportional to the Taylor number to the power ∼0.13 close to the exponent 1/7 highlighted by an analytical model. This small exponent traduces the control of heat transfers by the rotating viscous layer and thus may explain the difficulty met by engineers to develop strategies for the effective cooling of such rotating apparatus.