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Within a self-consistent thermal model using an isospin and momentumdependent interaction (MDI) constrained by the isospin diffusion data inheavy-ion collisions, we investigate the temperature dependence of the symmetryenergy $E_{sym}(\rho, T)$ and symmetry free energy $F_{sym}(\rho, T) $ for hot,isospin asymmetric nuclear matter. It is shown that the symmetry energy$E_{sym}(\rho, T)$ generally decreases with increasing temperature while thesymmetry free energy $F_{sym}(\rho, T)$ exhibits opposite temperaturedependence. The decrement of the symmetry energy with temperature isessentially due to the decrement of the potential energy part of the symmetryenergy with temperature. The difference between the symmetry energy andsymmetry free energy is found to be quite small around the saturation densityof nuclear matter. While at very low densities, they differ significantly fromeach other. In comparison with the experimental data of temperature dependentsymmetry energy extracted from the isotopic scaling analysis of intermediatemass fragments (IMF's) in heavy-ion collisions, the resulting density andtemperature dependent symmetry energy $E_{sym}(\rho, T) $ is then used toestimate the average freeze-out density of the IMF's.used to estimate theaverage freeze-out density of the IMF's.Comment: 9 pages, 7 figures, 1 figure added to show the temperature dependence  of the potential and kinetic parts of the symmetry energy. Revised version to  appear in PR

Temperature effects on the nuclear symmetry energy and symmetry free energy with an isospin and momentum dependent interaction