In this study, a modeling approach has been developed to take multiphysical effects into account in the prediction of the rotordynamic behavior of high speed minirotating machinery with a moderate flow confinement. The temperature increase in the confinement and the flow induced forces resulting from the surrounding fluid have been studied and these models are combined with the structural finite element models for determining the rotordynamic behavior. The structure has been analyzed via finite elements based on Timoshenko beam theory. Flow induced forces are implemented to the structure as added mass-stiffness-damping at each node representing the structure in the fluid confinement. A thermal model based on thermal networks in steady-state has been developed. This model is used to calculate the heat dissipation resulting from air friction and temperature increase in the air gap as a function of rotation speed. At each rotation speed, the temperature in the air gap between the rotor and stationary casing is calculated and air properties, which are used for the calculation of flow induced forces are updated. In this way, thermal and fluid effects in medium gap confinements are coupled with the rotordynamic model and their effects on stability, critical speeds, and vibration response are investigated. The experimental results are reported and compared with the theoretical results in an accompanying paper (Part II).