The influence of an exponentially decreasing temperature distribution on radiant interchange in a rectangular cavity is investigated using Ambarzumian's method. The rectangular cavity is defined by two semiinfinite parallel, diffuse gray surfaces, and a finite black surface. The radiosity at the edge of the cavity is shown to satisfy a nonlinear integral equation which is easily solved by iteration. For an isothermal cavity, the radiosity at the edge of the cavity is equal to the inverse of the square root of the emittance. Without calculating the radiosity distribution inside the cavity, the over-all heat transfer is expressed in terms of the radiosity at the edge of the cavity. Numerical results are presented for a wide range of temperature distributions and reflectances.