A previous analysis of turbulent heat transfer and flow with variable fluid properties in smooth passages is extended to flow over a flat plate at high Mach numbers. Velocity and temperature distributions are calculated for a boundary layer in which the effects of both frictional heating and external heat transfer are appreciable. The viscosity and thermal conductivity are assumed to vary as a power of the temperature, while the Prandtl number and specific heat are taken as constant. Skin-friction and heat-transfer coefficients are calculated and compared with the incompressible values. The relation between boundary-layer thickness and distance along the plate is obtained for various Mach numbers. The analytical results are compared with representative experimental data.