Based on the principle of double-lead worm gear meshing and the machining principle of double-lead involute worm gear, the tooth equation and mathematical equation of involute double-lead worm gear are established, in order to study the situation of double-lead worm gear under sunshine, thermal deformation error is introduced to establish a transmission error model about thermal deformation, and the effect of different temperatures on the double-lead involute worm gear transmission error is analyzed by ADAMS simulation, the results show that the average and maximum values of transmission error of double-lead involute worm gear increase with the decrease of temperature, and the mean square error of transmission error shows a slight increase with the increase of temperature. The results show that the mean and maximum values of the transmission error of the double-lead involute worm gear increase with the decrease of temperature, and the mean square deviation of the transmission error shows a slightly increasing trend with the increase of temperature.