Just reading my Science News ~ came in today's mail ~ they have an article about the Straits of Gibraltar. They formed 5.0 to 5.5 million years ago when the Atlantic cut through the uplift that'd earlier blocked the Mediterranean from the main body of the Ocean.
This lowered aggregate Ocean levels ~ and could have "cooled things down". The Ice Age started up 2.5 million years later ~
Almost everything I've read says scientists think the alteration of ocean currents, creating among other things the Gulf Stream, and divergence of salinity levels in the Atlantic and Pacific triggered the onset of the glacial cycles, but I can't tell you just how that worked.
It's interesting the opening of the Straits of Gibraltar came just before the Pliocene Warm. Any connection?