We have applied spectral‐transform methods to study three‐dimensional thermal convection with temperature‐dependent viscosity. The viscosity varies exponentially with the form exp(‐BT), where B controls the viscosity contrast and T is temperature. Solutions for high Rayleigh numbers, up to an effective Ra of 6.25×106, have been obtained for an aspect‐ratio of 5×5×1 and a viscosity contrast of 25. Solutions show the localization of toroidal velocity fields with increasing vigor of convection to a coherent network of shear‐zones. Viscous dissipation increases with Rayleigh number and is particularly strong in regions of convergent flows and shear deformation. A time‐varying depth‐dependent mean‐flow is generated because of the correlation between laterally varying viscosity and velocity gradients.