More on entropy function formalism for non-extremal branes
  We find R^4 correction to the non-extremal D1D5P solution of the supergravity by exactly solving the differential equations of motion and by using the entropy function formalism. In both cases, we find the same correction to the supergravity solution. We then calculate the correction to the entropy using the free energy method and the entropy function formalism. The results are the same. 
Mohammad R. Garousi, Ahmad Ghodsi, Tooraj Houri, Mehran Khosravi