5 by numerically finding the phase-space distribution func- tion. We show that the deformations in both momentum and real space becomes smaller and smaller as one in- creases the temperature. For homogeneous gases, we also calculate pressure, entropy, and heat capacity. In partic- ular, at low temperature limit and in weak interaction regime, we obtain an analytic expression for the entropy, which agrees qualitatively with our numerical result. The stability diagram for a trapped gas at finite temperature is also obtained. which the system becomes unstable. In Fig. 6, we plot the temperature dependence of the critical dipolar inter- action strength for various trap geometries. It can be seen that, independent of the trap aspect ratio λ , D ∗ t is an increasing function of T . This can be understood as higher temperature corresponds to smaller momentum and real space deformations, resulting in smaller dipolar interaction. In addition, higher temperature also yields higher kinetic energy which stabilizes the system. This work was supported by NSFC through grants 10974209 and 10935010, by the National 973 program (Grant No. 2006CB921205), and by the “Bairen” pro- gram of Chinese Academy of Sciences. To conclude, based on the semi-classical theory, we have studied the thermodynamics of a dipolar Fermi gas IV. CONCLUSIONS [1] K.-K. Ni, S. Ospelkaus, M. H. G. de Miranda, A. Pe’er, B. Neyenhuis, J. J. Zirbel, S. Kotochigova, P. S. Julienne, D. S Jin, and J. Ye, Science 322 , 231 (2008). [2] S. Ospelkaus, K.-K. Ni, M. H. G. de Miranda, B. Neyen- huis, D. Wang, S. Kotochigova, P. S. Julienne, D. S. Jin, J. Ye, Faraday Discuss. 142 , 351 (2009). [3] K.-K. Ni, G. Qu´ em´ ener, B. Neyenhuis, D. Wang, M. H. G. de Miranda, J. L. Bohn, J. Ye, and D. S. Jin, arXiv:0908.3931 (2009). [4] S. Ospelkaus, K.-K. Ni, D. Wang, M. H. G. de Miranda, B. Neyenhuis, G. Qu´ em´ ener, P. S. Julienne, J. L. Bohn, D. S. Jin, J. Ye, arXiv:0912.3854 (2009). [5] K. G´ oral, B.-G. Englert, and K. Rz¸a˙zewski, Phys. Rev. A 63 , 033606 (2001). [6] K. G´ oral, M. Brewczyk, and K. Rz¸a˙zewski, Phys. Rev. A 67 , 025601 (2003). [7] L. He, J.-N. Zhang, Y.-B. Zhang, and S. Yi, Phys. Rev. A 77 031605, (2008). [8] T. Miyakawa, T. Sogo, H. Pu, Phys. Rev. A 77 , 061603 (2008). [9] S. Ronen and J. L. Bohn, arXiv:0906.3753 (2009). [10] J.-N. Zhang and S. Yi, Phys. Rev. A 80 , 053614 (2009). [11] T. Sogo, L. He, T. Miyakawa, S. Yi, H. Lu, and H. Pu, New. J. Phys. 11 , 055017 (2009). [12] C.-K. Chan, C. Wu, W. Lee, and S. Das Sarma, arXiv:0906.4403 (2009). [13] L. You and M. Marinescu, Phys. Rev. A 60 , 2324 (1999). [14] M. A. Baranov, M. S. Mar’enko, Val. S. Rychkov, and G. V. Shlyapnikov, Phys. Rev. A 66 , 013606 (2002). [15] M.A. Baranov, L. Dobrek, and M. Lewenstein, Phys. Rev. Lett. 92 , 250403 (2004). [16] C. Zhao, L. Jiang, X. Liu, W. M. Liu, X. Zou, and H. Pu arXiv:0910.4775 (2009). [17] K. V. Samokhin and M. S. Mar’enko, Phys. Rev. Lett. 97 , 197003 (2006). [18] T. Shi, J.-N. Zhang, C.-P. Sun, and S. Yi, arXiv:0910.4051 (2009). [19] C. Wu and J. E. Hirsch, arXiv:0910.4940 (2009). [20] Equation (6) is different from that obtained in Ref. [9]. [21] A. L. Fetter and J. D. Walecka, Quantum theory of many- particle systems , (Dover Publications, Mineola, 2003).