Direct numerical solutions of the incompressible Navier–Stokes equations have been obtained under the Boussinesq approximation for the temporal evolution of a turbulent jet-like flow subjected to off-source volumetric heating, of the kind that occurs in a cloud due to latent heat release on condensation of water vapour. The results show good qualitative agreement with available experimental data on spatially growing jets. Thus, heating accelerates the flow and arrests jet growth; and turbulence velocities increase with heating but not as rapidly as mean velocities, so normalized intensities drop. It is shown that the baroclinic torque resulting from the heating enhances the vorticity dramatically in all three directions, with a preferential amplification at the higher wavenumbers that results in a rich fine structure at later times in the evolution of the jet. Streamwise vortex pairs, rendered stronger by mean flow acceleration, appear to be responsible for large expulsive motions at certain transverse cross-sections in the ambient fluid near the heated flow; together with the disruption of the toroidal component of the coherent vorticity achieved by heating, this results in an entraining velocity field that is qualitatively different from that around unheated turbulent jets. This mechanism may provide a plausible explanation for the experimentally observed drop in entrainment with off-source heating.