Residential fuel cell cogeneration is usually credited with all its recovered heat, although that heat is useful only if a coincident demand absorbs it. Hourly TRNSYS 18 simulations of an off-grid dwelling in Aomori City, Japan, with a 700 W proton exchange membrane fuel cell running on self-produced hydrogen, compared four dispatch rules, two thermal services and several electrolyzer and store sizes over a periodic year. With space heating, residual heat demand was 12.6 times the electrical deficit after photovoltaic and battery supply. The unit was potentially heat-rich in 88.7–92.3% of deficit hours with hot water alone and 2.2–3.7% with space heating. Against a run without hydrogen, 25–61% of the heat an immersed coil delivered to the store reduced unmet thermal demand where the cycle closed; 22–54% displaced solar heat and 15–22% raised tank losses. Under calendar dispatch with hot water alone, 75% of recovered heat could not pass the coil. Load following raised self-sufficiency from 88.9% to 96.3%, whereas calendar dispatch, and thermally led dispatch with space heating, needed 2.8–5.0 times the producible hydrogen. Electrode areas of 40–110 cm² gave identical service; each Nm³ of storage was below the seasonal swing of 76.7 Nm³ cost 1.77 kWh of output.