Using ab initio calculations we have investigated the thermal conductivity (κ) of diamond nanowires, unveiling unusual features unique to this system. In sharp contrast with Si, κ(T) of diamond nanowires as thick as 400 nm still increase monotonically with temperature up to 300 K, and room-temperature size effects are stronger than for Si. A marked dependence of κ on the crystallographic orientation is predicted, which is apparent even at room temperature. [001] growth direction always possesses the largest κ in diamond nanowires. The predicted features point to a potential use of diamond nanowires for the precise control of thermal flow in nanoscale devices.