Active cooling of thermoelectric generators (TEGs) is problematic since mechanical devices such as pumps and fans draw a high proportion of the limited power generated. Increasing the coolant fluid flow rate is typically a scenario of diminishing gains since the increased TEG power can be more than offset by the increase in power required for the fluid mover. Passive air cooling is an option, however the high air-side thermal resistance results in poor TEG power performance and low thermal efficiency. To address these issues, and others, a passive single phase liquid thermosyphon cooling system for use with TEGs has been designed, computationally simulated and experimentally tested. The novelty of the cooling system centres not only on the hot-side heat exchanger design, but also on the use of an open liquid reservoir as a dual-purposed heat store and air-side heat sink. This results in an effective source-to-sink heat exchange system that is entirely passive while providing effective cooling. This work describes the Simulation-Driven Design approach used to design the system for an example of a single TEG, experimental verification of the simulation results and TEG performance characteristics with the new cooling system.