Transient three-dimensional heat transfer between a traversing, structured, and rectangular object and an enclosure is studied. This study investigates the heat transfer process that occurs in brazing an aluminum heat exchanger in a controlled-atmosphere furnace. A model's development is discussed with prescribed enclosure temperature boundary conditions. The program determines the radiant heat exchange between gray diffuse surfaces, and solves the three-dimensional conduction equation for a solid with a radiant heat flux boundary condition using an implicit finite-difference method. The structured object's conduction and radiant thermal properties are described by effective values. It was shown that radiative thermal properties of the traversing object and the enclosure's temperature have a strong impact on the object's temperature history. The effective thermal emissivity was found to influence the object's rate of temperature change. The enclosure's temperatures influenced the object's equilibrium temperature. Also, it was shown that the object's position and rotation can alter its temperature distribution, but not as strong as the effect of boundary conditions and thermal properties. In addition to numerical methods, experiments were performed to further understand the process.