We investigate the upper bound on the vertical heat transportin thefully 3D Rayleigh–Bénard convection problem at the infinite Prandtl number fora micropolar fluid. We obtain a bound, given by the cube root of the Rayleigh num-ber, with a logarithmic correction. The derived bound is compared with the optimalknown one for the Newtonian fluid. It follows that the (optimal) upper bound for themicropolar fluid is less than the corresponding bound for the Newtonian fluid at thesame Rayleigh number. Moreover, strong microrotational diffusion effects can entirelysuppress the heat transfer. In the Newtonian limit our purely analytical findings fullyagree with estimates and scaling laws obtained from previoustheories significantlyrelying on phenomenology.