According to the ESRT, the rate of temperature increases below the Earth's surface is greatest between depths of

Between depths of tectonic plate boundaries and the outer core.

Explanation:

The rate of temperature increases below the Earth's surface is greatest between depths of tectonic plate boundaries and the outer core.  At the depth, some of the heat comes from the Earth's core while most of the heat comes from decay of radioactive elements, mainly uranium, thorium and potassium that is located in rocks of the crust. So we can say that the the increase in temperature with depth varies with the chemical composition and age of the rocks.