Adiabatic acceleration is employed to design the electron gun of HIRFL – CSR e –cooler by using the modified EGUN code. The electron beam transverse temperature variations with anode region and acceleration tube design parameters as well as the uniform solenoidal magnetic field are presented. Transversal temperature of less than 0.1eV at a maximum current density of 0.244A/cm2 are obtained over the full energy range of 2.75 ~ 165keV.