[en] In this article, three models with different isospin and momentum dependence are used to study the thermodynamical properties of asymmetric nuclear matter. They are isospin and momentum-dependent MDI interaction constrained by the isospin diffusion data of heavy ion collision, the momentum-independent MID interaction and the isoscalar momentum-dependent eMDYI interaction. Temperature effects of symmetry energy, mechanical and chemical instability and liquid-gas phase transition are analyzed. It is found that for MDI model the temperature effects of the symmetry energy attribute from both the kinetic and potential energy, while only potential part contributes to the decreasing of the symmetry energy for MID and eMDYI models. We also find that the mechanical instability, chemical instability and liquid-gas phase transition are all sensitive to the isospin and momentum dependence and the density dependence of the symmetry energy. (authors)