Numerical simulation of thermal convection induced by solvent evaporation in an initially isothermal fluid is considered. Both thermocapillarity and buoyancy driving forces are taken into account, and a criterium based on the Peclet number is used to analyze the stability of this transient problem. Critical Marangoni and Rayleigh numbers are obtained for a large range of Biot and Prandtl numbers. Results of the non-linear simulations are compared with a previous linear transient stability analysis based on a non-normal approach and with visualizations performed during polyisobutylene (PIB)/toluene solutions drying experiments. A scaling analysis is developed for the Marangoni problem and correlations are derived to predict the order of magnitude of temperature and velocity as a function of Bi, Ma and Pr numbers.