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.