Thermal desalination processes like membrane distillation (MD) aim to have rapid evaporation rates to provide large quantities of fresh water. These processes, which resemble counterflow-heat exchangers with membranes in the middle, conventionally seek to maximize vapor mass transfer while minimizing all other modes of heat transfer as "thermal losses." However, we can reverse this fundamental design need to make an exceptionally high throughput heat dissipation device. By using thin thermally conductive membranes and extremely rapid air flow rates, membrane heat exchangers inspired by MD can dissipate heat several times faster than conventional air-cooled heat exchangers. We demonstrate this new approach with discretized numerical modeling, multiphysics simulations, and a successful experimental demonstration using a sweep gas membrane distillation configuration. The experimental results show that, feed temperature, feed flow rate, sweep gas flow rate are the most influencing among the operating parameters on permeate flux. The multiphysics numerical simulation is carried out in COMSOL 6.0. To evaluate the potential of sweeping gas membrane distillation unit as a heat exchanger, the feed outlet temperature, evaporative heat flux and mass flux are studied with varying membrane thermal conductivity (0.2 - 200 W/mK). The mass flux and evaporative heat flux decreases as membrane thermal conductivity increases. However, the feed outlet temperature initially drops where evaporative cooling contributes much more to heat loss. Further increasing thermal conductivity reduces temperature and vapor pressure gradient across the membrane and resulting in reduced evaporative cooling and increased feed outlet temperature. In this scenario, higher sweep gas flow rate is recommended to deliver sufficient cooling. However, large pressure drops must occur in the air stream to deliver sufficient cooling. Furthermore, the evaporated fluid must either be lost, or recovered with a large system, such as the absorbing bottle used here. Overall, such enhanced heat exchange may hold promise in air-cooled devices that require lightweight design or portability.