DEEP earthquakes generally show fewer aftershocks and a larger variability in magnitude-frequency relations than shallow earthquakes(1-5). These characteristics and the factors that control them may place constraints on the mechanism of deep earthquakes, which is still uncertain(6-8). Here we show that systematic variations in aftershock productivity and magnitude-frequency relations are related to the temperature of the downgoing slab, as inferred from the vertical velocity and age of the subducting lithosphere. Deep earthquakes with substantial aftershock sequences are found only in colder slabs, and earthquakes in warmer slabs consistently show few aftershocks. Magnitude-frequency relations for deep earthquakes also show systematic variations as a function of slab thermal structure, with warmer slabs showing fewer small earthquakes (lower ’b-values’). The statistical properties of deep earthquakes thus appear to be temperature sensitive to an extent not observed for shallow earthquakes, and not adequately explained by simple geometrical limitations on fault width.