The Mohorovicic Discontinuity has a temperature ranging from 500-600 degrees C (celsius) for the sections of the base of the crust that are under the continents, and 150-200 degrees C in the areas that are under the oceans. The Discontinuity itself is more of an interface between the layers of the crust and the mantle than a layer itself, so it is difficult to say what is the answer to the question of its thickness. The best estimate seems to be that a transition layer between the two averages around 500 meters.
The Mohorovicic Discontinuity is the term for the boundary between Earth's crust (the layer that is immediately below the surface) and the uppermost layer of Earth's mantle. Together these make up the lithosphere. The term "discontinuity" is used in geology to mean an area where seismic waves change velocity. The Mohorovicic Discontinuity was discovered in 1909 because of this property of wave velocity changes, by a Croatian scientist for whom it is now named.