This paper presents the design of a compact (~1 cm³) thermoelectric (TE) generator intended to generate power locally for sensor/electronic device applications using hot gases (~100°C to 400°C). The design employs 13-mm-diameter, ~0.36-mm-thick (48 mm³) silicon-micromachined TE modules that are stacked to form a cylindrical, finned heat exchanger. The stacked structure is intended to establish a large, uniform temperature gradient across radially oriented thermopiles in each module. Analytical heat transfer and electrical circuit models are used to design and optimize the thermopile for maximum output power under microfabrication and system-level constraints. Optimized structures using PbTe and Bi₂Te₃ thin films are predicted to achieve output power levels of 1.3 mW per module (26.7 mW/cm³) and 0.83 mW per module (17.4 mW/cm³), respectively, for hot gas at 400°C.