The synthesis of extensive sea-floor heat-flow and subsidence data for the North Atlantic and North Pacific Oceans reveals that these quantities approach equilibrium values before the oceanic lightosphere is 80 million years old. These are fundamental constraints on any model describing the thermal evolution of the oceanic lithosphere, but previously they have not been well established and have been ignored in recent thermal models. To satisfy these constraints, either the lithosphere must establish the asthenosphere, or a tenuous set of conditions interrelating plate thickness, density changes, basal heat flow, and asthenosphere temperature gradients must prevail. Failure to recognize this has led to the acceptance of thermal models that are inconsistent with a vast amount of oceanographic data.