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A compressible laminar boundary layer developing over an isotropic porous substrate is investigated by asymptotic and numerical methods. The substrate is modeled as an array of cubes. The momentum and enthalpy balance equations are derived by volume averaging. The self-similar solution proposed by Tsiberkin (2018) [Transp. Porous Media 121(1):109-120] for streamwise-growing permeability is extended to include compressibility, heat conduction and a nonlinear drag. The velocity profile shows an inflection point at the free fluid-porous interfacial layer, below which it decreases to zero. A marked reduction of the adiabatic recovery temperature of the fluid and the velocity gradient at the interface is observed for high porosity, large grains and relatively high Mach numbers. The temperature imposed at the bottom of the porous substrate has a negligible influence on the shear stresses.