We have applied spetral-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. ¿American Geophysical Union 1995