r$_{+}$ < r$_{1ext}$ or r$_{+}$ > r$_{2ext}$ for hyperbolic black branes. We found that the existence of r$_{ext}$ for k = 0, and r$_{1ext}$ for k = − 1 depends on the value of α . For the case of k = 0 with large values of α ( α > α$_{ext}$ ), one can have black brane with any size. This feature shows that dilaton change the thermodynamics of black branes drastically. In this case, the temperature goes to infinity as r$_{+}$ goes to zero for n > 4, while it approaches to a constant for n = 4. For the case of k = − 1, one may have small black branes provided α$_{1ext}$ < α < α$_{2ext}$ , while large black branes exist for any value of α . Again, this is a drastic change in the properties of the solutions because of the dilaton field. We analyzed the thermal stability of the solutions in the canonical ensemble by finding a Smarr-type formula and considering ( ∂ $^{2}$M/∂S$^{2}$)$_{Q}$ for the charged topological dilaton black brane solutions in ( n +1) dimensions. We showed that for the case of k = 0, small black branes are unstable for α$_{ext}$ < α < α$_{crit}$ , while they are stable for α > α$_{crit}$ . Also, in this case large black branes are stable for arbitrary α . For the case of k = − 1, small black branes are unstable, while large ones are stable. That is dilaton with the potential given in Eq. (2), changes the stability of the black branes drastically. We thank the referees for constructive comments. This work has been supported by Research Institute for Astronomy and Astrophysics of Maragha, Iran. [1] J. M. Maldacena, Adv. Theor. Math. Phys. 2 , 231 (1998); E. Witten, Adv. Theor. Math. Phys. 2 , 253 (1998); S. S. Gubser, I. R. Klebanov and A. M. Polyakov, Phys. Lett. B 428 , 105 (1998). [2] M. Hennigson and K. Skenderis, J. High Energy Phys. 07 , 023 (1998); R. B. Mann, Phys. Rev. D 60 , 104047 (1999); R. Emparan, C. V. Johnson and R. Meyers, Phys. Rev. D 60 , 104001 (1999); R. B. Mann, Phys. Rev. D 61 , 084013 (2000); S.Y. Hyun, W.T. Kim and J. Lee, Phys. Rev. D 59, 084020 (1999); V. Balasubramanian and P. Kraus, Commun. Math. Phys. 208 , 413 (1999); S. N. Solodukhin, Phys. Rev. D 62 , 044016 (2000); 18 Acknowledgments