A three‐dimensional direct numerical simulation (using a fully spectral method) of compressible convection of an infinite Prandtl number fluid in a wide box with dimensions 5×5×1 was conducted. Depth‐dependent viscosity, thermal expansivity, and thermal conductivity have been included in order to model deep‐seated processes in the Earth’s mantle. Solutions have been obtained up to a surface Rayleigh number of 4×107. There is a remarkable contrast between the dynamics of the upper and lower boundary layers. Very few cylindrical plumes are developed at the bottom but they merge collectively to form a strong upwelling, which pulses chaotically. Viscous and adiabatic heating are found to become important at high Rayleigh numbers, larger than 107. These results have important implications on the thermal structure of early Earth, where there might have been dramatic effects from intense mechanical heating near the top boundary layer.