The development of mathematical models plays a fundamental role in the design, optimization, and control of processes. Regarding heat transfer in moving bed reactors, the chemical reaction implies the inclusion of a nonhomogeneous and nonlinear term in model equations, making the analytical integration a very difficult task. Up to date, there is not an analytic and/or a semi-analytic solution to a heat transfer model of a moving bed reactor (MBR) with isothermal walls to the distributed parameters in the solid phase. Therefore, starting from analytical solutions of the associated homogeneous (linear) problems and through the spectral expansion of the nonhomogeneous vector, this work presents strategies for determining semi-analytical solutions of nonhomogeneous and nonlinear problems. An MBR with a first-order chemical reaction in the solid phase—kaolinite dehydroxylation in the kaolinite flash calcination process—is selected as the case study; however, the strategies can easily be applied to other nonlinear models. Results for conversion, and fluid and particle temperatures, are given for different parameter values. The solutions perform stable, fast, and accurate. When compared with a hybrid finite difference and finite analytic (FD&FA) numerical method, the solution showed a very good agreement.