Abstract Unsteady, axisymmetric fluid flow and heat transfer in a droplet rapidly solidifying on a cold substrate are investigated. The thermal and solutal Marangoni forces along the droplet surface are the driving forces for fluid motion. Concentration of the insoluble surfactants are determined by surface convection and diffusion. The solidification is governed by an instantaneous nucleation and a subsequent continuous growth induced by a given nucleation temperature. Solute trapping is also accounted for. By using a curvilinear orthogonal toroidal coordinate system, the computed results show that the effects of the supercooling and nucleation temperature, Marangoni, Stefan, Prandtl numbers, ratio of the changes in surface tension due to concentration and temperature gradients, and the contact angle of the droplet on unsteady flow and thermal patterns, distributions of surfactant concentration, cooling effects, recalescence and growth rates. Temperature variations at the axisymmetric axis agrees well with a one-dimensional model. A systematical confirmation and evaluation of surface tension due to solute concentration is also provided.