A numerical analysis is presented of free surface profiles, Marangoni convection and the temperature distribution in electrostatically levitated droplets. The analysis is based on the boundary element solution of electric potential outside the droplet, the weighted residuals formulation of the free surface balance equation involving electrostatic stresses, surface tension and gravity, and the finite element solution of the internal fluid flow and temperature distribution in the electrostatically deformed droplets. Numerical simulations are carried out for several different materials and various operating conditions. Results show that an applied electrostatic field generates a normal stress distribution along the droplet surface, which, combined with surface tension, causes the droplet to deform into an ellipsoidal shape in microgravity and into the shape of a blob with the lower side being flatter under terrestrial conditions. Laser heating induces a non-uniform temperature distribution in the droplet, which in turn produces recirculating convection in the droplet. For the cases studied, Marangoni convection is the predominant mode and buoyancy effects are negligible. It is found that there is a higher temperature gradient and hence stronger Marangoni convection in droplets with higher melting points which require more laser power. The internal recirculating flow may be reduced by more uniform laser heating. During undercooling of the droplet with heating turned off, both temperature and fluid flow fields evolve in time, such that the temperature gradient and the tangential velocities along the droplet surface subside in magnitude and reverse their directions.