An oscillatory instability mechanism is identified for a horizontal liquid layer with
undeformable open surface heated from the air side. Although buoyancy and surface
tension gradients are expected to play a stabilizing role in this situation, we show that,
acting together, they may lead to the instability of the motionless state of the system.
The instability is a consequence of the coupling between internal and surface waves,
whose resonant interaction and resulting mode mixing are discussed. Predictions
amenable to experimental test are given together with a thorough analytical and
numerical study of the problem.