A theoretical model is proposed to describe the entrainment of ambient air by a rising thermal. The model is appropriate for the first few revolutions of a strongly heated thermal whose motion is dominated by its initial conditions. At sufficiently early times, only the outer edge of the thermal is turbulent. The ambient gas mixes with the thermal gas along the turbulent interface and is convected into the thermal along streamlines. The gas densities and species concentrations on each streamline are obtained by superimposing a turbulent mixing layer on the edge of Hill's spherical vortex. Solutions are obtained in terms of the dimensionless ratio of the mixing length to the thermal radius(l/a )and the entrainment coefficient is shown to be directly proportional tol/a.