Exact solutions of the laminar-boundary-layer equations for wedge-type flow with constant property values are presented for transpiration-cooled surfaces with variable wall temperatures. The difference between wall and stream temperature is aussumed proportional to a power of the distance from the leading edge. Solutions are given for a Prandtl number of 0.7 and ranges of pressure-gradient, cooling-air-flow, and wall-temperature-gradient parameters. Boundary-layer profiles, dimensionaless boundary-layer thicknesses, and heat-transfer coefficents are given in both tabular and graphical form. Corresponding results for constant wall temperature and for impermeable surfaces are included for comparison purposes.