A differential Reynolds stress and heat flux closure is adopted for modelling the turbulent transport of heat and momentum in vertical buoyant free plumes. Modelled transport equations are solved for the turbulent stresses and heat fluxes, the turbulence energy dissipation rate, and the mean-square temperature fluctuations. Closure at this level permits the turbulent transport processes to be treated more exactly than with Boussinesq-type two-equation models which are based on the notion of an effective viscosity and diffusivity. The solution of a transport equation for the thermal dissipation rate, which avoids the need to empirically prescribe the ratio of the thermal and mechanical time scales, is also investigated. The model is applied to the calculation of both self-similar plumes and forced plumes. The results are compared with existing experimental data and are found to be in reasonable agreement with the measured behaviour.