We have investigated the dynamics and heat-transfer of 3-D mantle convection with a realistic temperature-and pressure-dependent conductivity in a constant viscosity medium. Variable thermal conductivity is found to stabilize greatly the interior flow and the boundary-layer dynamics, as compared to constant conductivity solutions for Rayleigh number up to 5¿105. Due to the nonlinear interaction between variable conductivity and convective flow, a great deal of heat can be transported coherently through the mantle within thick pipe-like structures with a radius of around 500 km. These pipe-like solutions can be understood from the intermediate asymptotic nature of the nonlinear heat diffusion equation. We suggest that these thick plume-like structures in the lower mantle imaged recently by tomography may be a manifestation of this nonlinearity in the conductivity of the temperature equation. ¿ 2000 American Geophysical Union