We investigate the influence of heating on the shape and dynamics of a droplet on a liquid substrate. The problem is studied numerically in the framework of longwave amplitude equations. The effect of gravity is taken into account. We show that the thermocapillary stresses produce a significant deformation of the droplet's interfaces. Heating the droplet from above can create an oscillatory instability generating periodic and quasiperiodic oscillations, change of droplet shape, and droplet decomposition. Heating from below can lead to the substrate layer's rupture due to its monotonic instability.
