The complexities of analyzing rolling element bearings vary. Vendors offer cataloged solutions comprised of limiting loads and speeds, bearing life, and lubricant recommendations. These guidelines meet the needs of most customers; however, more demanding applications warrant advanced analyses. This work focuses on thermal management. Current literature offers system level solutions using either resistance methods or finite element analysis (FEA). Resistance methods have rapid computation time, yet lack accuracy. Finite element methods improve the accuracy, but are computationally cumbersome. This work proposes an integral transform method. The rapidly computed solution yields accurate results. The methodology and results of this work are presented in a three-part series. Part I details existing literature and provides the framework for a new heat transfer model. This model describes rolling-element bearing systems containing a shaft, housing, and numerous bearing raceways. It also includes gears, cooling jackets, and is applicable for several methods of lubrication. The model consists of solid component partial differential equations (PDEs) in conjunction with analytic expressions for fluid temperatures, convection equation, and mass flow. Part II presents the housing, shaft, and bearing raceway PDE solutions. Part III offers experimental validation, as well as observations from experiments on fluid flow within the bearing.