It is easy to see from the map that certain currents are warm, while others are cold. The reason for this is simple: the currents that move from equator towards the poles are warmer. They carry warm water towards the cold oceans. This warm water has been generated due to the insolation from the sun. eg. Gulf Stream, Kurushio etc.

The cold currents originate at the poles and descend towards the equator, as seen in the image. Eg. Oyashio, Labrador current.

The currents deflect due to the rotation of the earth and direction of the wind. The wind circles around low and high pressure areas, changing the direction of the current. Also, the Coriolis Force influences their direction.