Thermal action and specific heat of the five-dimensional non-extremal black hole

We construct the Euclidean on-shell action for the five-dimensional non-extremal black hole with multiple electric charges. We show that this thermal action agrees with one-half of the entropy. This agreement is argued to be related to the generalized Smarr formula of the five-dimensional black hole mass. Through the calculation of the specific heat far off extremality we observe that a phase transition occurs.