It is commonly supposed that plate tectonic rates are controlled by the temperature‐dependent viscosity of Earth's deep interior. If this were so, a small decrease in mantle temperature would lead to a large decrease in global heat transport. This negative feedback mechanism would prevent mantle temperatures from changing rapidly with time. We propose alternatively that convection is primarily resisted by the bending of oceanic lithosphere at subduction zones. Because lithospheric strength should not depend strongly on interior mantle temperature, this relationship decreases the sensitivity of heat flow to changes in interior mantle viscosity, and thus permits more rapid temperature changes there. The bending resistance is large enough to limit heat flow rates for effective viscosities of the lithosphere greater than about 10²³ Pa s, and increases with the cube of plate thickness. As a result, processes that affect plate thickness, such as small‐scale convection or subduction initiation, could profoundly influence Earth's thermal history.