The analytical theory of the “passive thermal design of spacecraft" can be divided into two parts. The first part is concerned with the description of the radiant heat transfer to spacecraft external surfaces. The second part is concerned with calculating temperature over a spacecraft when the radiant heat incident, on the spacecraft's wall, is known. The first part, the calculation of the heat incident on a spacecraft's external surfaces, has been investigated in the literature. References one, two, and three are examples of such papers. Unfortunately, the results of auch papers are either numerical or else too specialized to be of general interest for the analytical study of the thermal design of spacecraft. The second part, the calculation of temperatures over a spacecraft when the incident radiant heat is known, is also dealt with in the literature. References four and five are examples of such papers. The heat flow, occurring in the walls of spacecraft, is nonlinear because of thermal radiation and few exact solutions are known. This problem is usually attacked by "linearizing'' the nonlinear term or by directly employing power aeries. The solution of the nonlinear heat equation by the linearization process is valid only for small temperature variations. When temperature differences are large, the linearized solutions do not properly account for the nonlinear radiation terms and series error can result. When power series are employed directly to solve the nonlinear heat flow equation, the labor required to solve the time dependent problem is generally excessive because the elementary functions cannot be used efficiently. In this thesis, the radiant heat transferred to spacecraft is found by the use of Fourier series. The resulting solutions are simple and are valid for spacecraft of very general geometry. Heat transfer calculation which previously required extensive integration on electronic computers can be calculated by the results of this thesis with only trivial labor. Also, the results have the advantage of being well suited for use in the solution of the nonlinear heat transfer equation. The problem of heat flow including nonlinear radiation is also attached in this thesis. The method of solution used is closely related to the well known method of successive approximations and allows solution of nonlinear equations which do not have the classical “Small perturbation parameter.” Also, the method of solution used makes good use of the elementary functions so that time dependent problems can be solved without excessive labor. The problems solved in this thesis includes: the temperature time history of a body at uniform temperature but exposed to periodic radiative heating, the temperature time history of a body having nonuniform temperatures and exposed to periodic radiative heating, and finally the problem of linear heat flow with nonlinear boundary conditions. In each case it is shown how linearized solutions neglect the important results of nonlinear radiation heat transfer. / Master of Science