The LOD is really shorthand for small *changes* in angular momentum of the planet. Many people realize that disturbances such as volcanic eruptions, earthquakes, and tsunamis can alter the moment of inertia of the earth enough that, together with the laws of conservation of momentum and energy that the length of day (LOD) will change slightly. If the LOD increases, then the earth has lost angular kinetic energy, and if it has decreased, then the earth has gained some.
Now, whether this is a real connection or just coincidence, what Dickey and others have observed is that the average temperature of the earth's surface will proportionally follow this change in LOD, with a slight lag. This is a JPL graph, where CAM represents an angular momentum
Whether this is poleward motion of water that changes both the angular momentum of the planet along with an average temperature, no one really knows but they think that may be too small an effect. More likely, Dickey indicated it still could be some internal mantle-related effects which then can have an effect on climate through changes in magnetic shielding. And I believe that nad brought that up on another thread.