More general Lovelock gravity permits combinations of higher order power of R, such as R4-type terms, which can also evade higher than second order derivatives with respect to the metric [14]. In type II-B and heterotic string theo-ries, the Gauss–Bonnet term is the next to leading order correc-tion to Hilbert–Einstein term. The Gauss–Bonnet term is free of ghosts when expanding on the Minkowskian background, without the problems of unitarity. A static, spherically symmetric solution of Gauss–Bonnet gravity is obtained in [15]. This solution is ex-tended by including a cosmological constant [16]. We call this so-lution Boulware–Deser–Cai solution. Here we use thermodynamic method to derive this solution.