[en] The temperature of electron beam is an important parameter in electron cooling device. Transverse temperature will be reduced when an electron beam passes through a negative gradient magnetic field. Some theoretical approaches on adiabatic expansion are presented here. Adiabatic expansion of the electron beam moving in different magnetic fields with different energy and current was investigated by computer simulation. The results show that the transverse temperature of the electron beam is reduced by a factor equal to the ratio between the initial and final magnetic field strengths, provided that the field change is adiabatic with respect to the cyclotron motion of the electrons