  Two derivative Jackiw Teitelboim gravity theory captures the near horizon
dynamics of higher dimensional near extremal black holes, which is governed by
a Schwarzian action at the boundary in the near horizon region. The partition
function corresponding to this boundary action correctly gives the statistical
entropy of the near extremal black hole. In this paper, we study the
thermodynamics of spherically symmetric four dimensional near extremal black
holes in presence of arbitrary perturbative four derivative corrections. We
find that the near horizon dynamics is again captured by a JT like action with
a particular namely square of Ricci scalar higher derivative modification.
Effectively the theory is described by a boundary Schwarzian action which gets
suitably modified due to the presence of the higher derivative interactions.
Near extremal entropy, free energy also get corrected accordingly.
