During the early Pliocene, 5 to 3 million years ago, globally averaged temperatures were substantially higher than they are today, even though the external factors that determine climate were essentially the same. In the tropics, El Niño was continual (or ``permanent'') rather than intermittent. The appearance of northern continental glaciers, and of cold surface waters in oceanic upwelling zones in low latitudes (both coastal and equatorial), signaled the termination of those warm climate conditions and the end of permanent El Niño. This led to the amplification of obliquity (but not precession) cycles in equatorial sea surface temperatures and in global ice volume, with the former leading the latter by several thousand years. A possible explanation is that the gradual shoaling of the oceanic thermocline reached a threshold around 3 million years ago, when the winds started bringing cold waters to the surface in low latitudes. This introduced feedbacks involving ocean-atmosphere interactions that, along with ice-albedo feedbacks, amplified obliquity cycles. A future melting of glaciers, changes in the hydrological cycle, and a deepening of the thermocline could restore the warm conditions of the early Pliocene.