When hydrogen gas is used or stored within a building, as with a hydrogen-powered vehicle parked in a residential garage, any leakage of unignited H2 will mix with indoor air and may form a flammable mixture. One approach to safety engineering relies on buoyancy-driven, passive ventilation of H2 from the building through vents to the outside. To discover relationships between design variables, we combine two types of analysis: (1) a simplified, 1-D, steady-state analysis of buoyancy-driven ventilation and (2) CFD modeling, using FLUENT 6.3. The simplified model yields a closed-form expression relating the H2 concentration to vent area, height, and discharge coefficient; leakage rate; and a stratification factor. The CFD modeling includes 3-D geometry; H2 cloud formation; diffusion, momentum, convection, and thermal effects; and transient response. We modeled a typical residential two-car garage, with 5 kg of H2 stored in a fuel tank; leakage rates of 5.9 to 82 L/min (tank discharge times of 12 hours to 1 week); a variety of vent sizes and heights; and both isothermal and non-isothermal conditions. This modeling indicates a range of the stratification factor needed to apply the simplified model for vent sizing, as well as a more complete understanding of the dynamics of H2 movement within the building. A significant thermal effect occurs when outdoor temperature is higher than indoor temperature, so that thermocirculation opposes the buoyancy-driven ventilation of H2. This circumstance leads to higher concentrations of H2 in the building, relative to an isothermal case. In an unconditioned space, such as a residential garage, this effect depends on the thermal coupling of indoor air to outdoor air, the ground (under a concrete slab floor), and an adjacent conditioned space, in addition to temperatures. We use CFD modeling to explore the magnitude of this effect under rather extreme conditions.