In the absence of natural convection, efficient heat transfers rely on externally forced flows. Generating such flows with acoustic waves rather than mechanical fans would enable remote locations to be cooled using virtually infinite lifetime transducers. This outlook is reinforced by the recent discovery that standing acoustic waves drive streaming flows of much higher velocities if the background medium is inhomogeneous. This regime of streaming is investigated experimentally in a cavity filled with stably-stratified air in which horizontal sound waves are found to significantly enhance heat transfers. The additional heat flux scales as the square of the input acoustic power for low amplitude waves and increases with the air stratification. These two features qualitatively match theoretical predictions, although corrections possibly ascribed to gravity are observed.