With the improvement of experimental techniques and the replacement of equipment

composition and application of solid material have been gained a series new development. So there is continuing interests in polaron. N.Tokuda discussed that the variational law of the ground-state energy

the excited state energies with coupling constant; Xiao Jing-lin

et al

. investigated that the properties of polaron in various coupling strength; Xiao Wei

et al

. studied that the affact of temperature on polaron; We discussed that the properties of acoustic deformation potential polaron. This paper was going to illustrate the variational law of the effective mass of polaron with temperature and coupling strength.In this paper

the variational relation of the effective mass of polaron in crystals with temperature and coupling strength was derived by using linear-combination operator and unitary transformation method. The results indicated that the effective mass increases with increasing coupling strength when temperature is constant

resulting in the interaction of electron phonon strengthens with increasing coupling strength. The results also illustrate that the effective mass varies with variation of temperature when coupling strength is constant

the stronger coupling strength is

the more obvious the affect of temperature on effective mass. At limit of weak-coupling

the effective mass of slow moving polaron has nothing to do with temperature because a electron is approximate a free-electron at limit of weak coupling and it’s motion is not affected by crystals vibration.In sum

the effective mass of polaron increases with increasing coupling strength when temperature is constant

and affect of temperature on effective mass also increases with increasing coupling strength.