Low-temperature heat is abundant, accessible through solar collectors or as waste heat from a large variety of sources. Thermoacoustic engines convert heat to acoustic work, and are simple, robust devices, potentially containing no moving parts. Currently, such devices generally require high temperatures to operate efficiently and with high power densities. Here, we present a thermoacoustic engine that converts heat to acoustic work at temperature gradients as low as similar to 4-5 K/cm, corresponding with a hot-side temperature of similar to 50 degrees C. The system is based on a typical standing-wave design, but the working cycle is modified to include mass transfer, via evaporation and condensation, from a solid surface to the gas mixture sustaining the acoustic field. This introduces a mode of isothermal heat transfer with the potential of providing increased efficiencies - experiments demonstrate a significant reduction in the operating temperature difference, which may be as low as 30 K, and increased output - this 'wet' system produces up to 8 times more power than its dry equivalent. Furthermore, a simplified model is formulated and corresponds quite well with experimental observations and offering insight into the underlying mechanism as well as projections for the potential performance of other mixtures. Our results illustrate the potential of such devices for harvesting energy from low-temperature heat sources. The acoustic power may be converted to electricity or, in a reverse cycle, produce cooling - providing a potential path towards solar heat-driven air conditioners.