A dynamic model predicting human thermal responses in cold, cool, neutral, warm, and hot environments is presented in a two-part study. This, the first paper, is concerned with aspects of the passive system: 1) modeling the human body, 2) modeling heat-transport mechanisms within the body and at its periphery, and 3) the numerical procedure. A paper in preparation will describe the active system and compare the model predictions with experimental data and the predictions by other models. Here, emphasis is given to a detailed modeling of the heat exchange with the environment: local variations of surface convection, directional radiation exchange, evaporation and moisture collection at the skin, and the nonuniformity of clothing ensembles. Other thermal effects are also modeled: the impact of activity level on work efficacy and the change of the effective radiant body area with posture. A stable and accurate hybrid numerical scheme was used to solve the set of differential equations. Predictions of the passive system model are compared with available analytic solutions for cylinders and spheres and show good agreement and stable numerical behavior even for large time steps.