A binary mixture of dimyristoylphosphatidylcholine (DMPC) and cholesterol displays a fluid miscibility gap under excess water conditions. Effects due to the imperfect miscibility of the two amphiphiles are studied near to and far from thermodynamic equilibrium by time-resolved small angle x-ray diffraction. The experiment discloses that this mixture phase separates when leaving the miscibility gap upon heating, a transition that is not included in current phase diagrams. This transition appears to be reversible and shows a temperature hysteresis of only a few degrees. We suggest a model in which the transition is driven with increasing temperature by a movement of the cholesterol away from the hydrophilic-hydrophobic interface toward the hydrophobic core of the bilayer.