The paper examines the role of heat diffusion as an internal noise source in aeroengines and as a source of noise in the mixing of hot jets. We consider a number of model problems and find that the sound induced by unsteady heat transfer can show an unusually weak dependence on the mean flow velocityU, the intensity scaling asU3in three dimensions. At low enough velocities diffusion effects will overwhelm other noise sources, but we have failed in our search for a significant practical situation in which we can prove that sound generated by diffusion clearly dominates over that excited by unsteady aerodynamic forces; they are sometimes comparable.We examine the possibility that diffusive monopole sources feature in the noise of hot jets using model problems in the linear case and using dimensional analysis in the nonlinear case, and conclude that no significant monopole exists when the specific heats are constant. But they are not constant at low frequencies when, for example, heat flows into and out of vibrational energy modes; then an important monopole source is present. This source shows an unusually complicated scale effect.