The axial symmetry breaking of steady thermocapillary flow in a sessile droplet with wetting radius R of a non-volatile liquid with thermal diffusivity κ and temperature coefficient of surface tension γ on a plane solid substrate with a constant temperature Tw is investigated numerically by means of linear stability analysis. An indeformable spherical free surface of the droplet is assumed. The heat transfer between the free surface and the ambient gas at a uniform temperature Ta is modeled using Newton’s law of cooling. The dependence of the critical Marangoni number Mac = ΔTc γ R/(µκ) on the contact angle α and the Prandtl number Pr is computed, where ΔT = |Tw − Ta|. We consider both cases, when the substrate is either hotter (Tw > Ta) or colder (Tw < Ta) than the ambient. For a hot substrate, small contact angles (α < 10°) and sufficiently large Prandtl numbers (Pr > 0.75) we find non-axisymmetric steady Benard−Marangoni cells near the center of the droplet. When the contact angle is increased beyond α > 13° the critical mode starts rotating and the critical wave number m depends sensitively on α. Mac increases strongly for α > 18° (fig. 1a). For non-wetting droplets (α > 90°) and low Prandtl numbers (Pr < 0.06) we find a steady thermocapillary instability for both hot and cold substrates. In the latter case the critical curve Mac(Pr) turns backwards (fig. 1b), leading to a linear stabilization of the axisymmetric flow upon increasing the Marangoni number. For still higher Marangoni numbers and higher contact angles oscillatory critical modes can arise. In the talk, stability boundaries, modal structures and physical mechanisms shall be addressed.