The dynamics of evaporating water droplets deposited on a heated substrate is investigated numerically. Droplets are pinned with a contact line radius of R = 1 mm. Evaporative mass flow and convection occurring inside the droplets are studied for different heating substrate sizes L-S and heating temperatures T-S. A simplified model neglecting hydrodynamics in air and evaporative cooling and assuming droplets to be spherical caps is simulated with a finite element method. A toruslike convective cell appears inside the droplets as evaporation takes place. For L-S/R > 1, the contact line is warmer than the apex of the droplets, and convection generates a downstream flow in the vicinity of the symmetry axis of the droplets. For L-S/R < 1, it is the apex that is warmer. Convection then generates an upstream flow. The overall evaporation time is described. It slows when L-S/R > 1.