Residual amplitude modulation (RAM) in electro-optical phase modulators (EOM) and its influence on the laser frequency shift of iodine-stabilized 532 nm laser are investigated experimentally. The relationships between the EOM crystal temperature and the RAM, as well as stabilized laser frequency are observed. The effects and problems of using active voltage feedback method to suppress the RAM are researched. An active temperature feedback method is proposed and demonstrated to suppress the RAM fluctuation by controlling the EOM temperature. With this method the suppression of the fundamental component in the RAM spectra overtakes 40 dB. The RAM fluctuation is controlled effectively, and additional frequency fluctuation is induced from adopting the system. The laser frequency stability can achieve or be better than 5×10-15 for the averaging time from 100 s to 104 s, and the stability of indine-stabilized 532 nm laser frequency in a medium and long term is improved greatly.