Two-dimensional surface-tension-driven Bénard convection in a layer with a free-slipbottom is investigated in the limit of small Prandtl number using accurate numericalsimulations with a pseudospectral method complemented by linear stability analysis and aperturbation method. It is found that the system attains a steady state consisting ofcounter-rotating convection rolls. Upon increasing the Marangoni number Mathe system experiences a transition between two typical convective regimes. The first one isthe regime of weak convection characterized by only slight deviations of the isotherms fromthe linear conductive temperature profile. In contrast, the second regime, called inertialconvection, shows significantly deformed isotherms. The transition between the two regimesbecomes increasingly sharp as the Prandtl number is reduced. For sufficiently small Prandtlnumber the transition from weak to inertial convection proceeds via a subcriticalbifurcation involving weak hysteresis. In the viscous zero-Prandtl-number limit thetransition manifests itself in an unbounded growth of the flow amplitude for Marangoninumbers beyond a critical value Mai. For Ma<Mai thezero-Prandtl-number equations provide a reasonable approximation for weak convection atsmall but finite Prandtl number. The possibility of experimental verification of inertialBénard–Marangoni convection is briefly discussed.