  Using the energy method we investigate the stability of pure conduction in
Pearson's model for B\'enard-Marangoni convection in a layer of fluid at
infinite Prandtl number. Upon extending the space of admissible perturbations
to the conductive state, we find an exact solution to the energy stability
variational problem for a range of thermal boundary conditions describing
perfectly conducting, imperfectly conducting, and insulating boundaries. Our
analysis extends and improves previous results, and shows that with the energy
method global stability can be proven up to the linear instability threshold
only when the top and bottom boundaries of the fluid layer are insulating.
Contrary to the well-known Rayleigh-B\'enard convection setup, therefore,
energy stability theory does not exclude the possibility of subcritical
instabilities against finite-amplitude perturbations.
