It is usually assumed that tunneling current is fairly independent of temperature. By performing an atomistic transport simulation, we show, to the contrary, that the subthreshold tunneling current in a graphene nanoribbon (GNR) band-to-band tunneling transistor (TFET) should show significant and non-linear temperature dependence. Furthermore, the nature of this non-linearity changes as a function of source/drain doping and vertical electric field, indicating that such non-linearity, if properly understood, may provide important insights into the tunneling phenomena. Finally, by developing a pseudo-analytical method, we predict that such temperature dependence is not unique to GNR but should rather be a general behavior for any band-to-band tunneling transistor independent of the channel material.