The Miocene is not a period, it is an epoch ranging from 23.4 Mya to 5.3 Mya, it's divided into six stages (or ages). The Miocene and the Pliocene together form the Neogene period.
The Miocene is a bit of a bugger climatologically, generally the early part of the epoch sees a cooling as the Antarctic ice sheet established in the Eocene grew and the establishment of the circumpolar current in the Antarctic Ocean, but at the same time the proto-Mediterranean dried out entirely as the Alps rose which caused temperatures across Eurasia to rise. The later Miocene is generally warmer than the present climate.
Work done in 2011 in Bremerhaven suggests the warming climate in the late Miocene can be put down to changes in vegetation patterns across the world causing a slight darkening of the planet.