We developed a two-stage temperature control system for a long-term stable measurement of AMoRE neutrinoless double beta decay experiment using a dilution refrigerator. The first-stage control was made with a standard PID system using an AC bridge with a ruthenium oxide thermometer as the main thermometer of the mixing chamber plate. The second-stage control was obtained with a magnetic microcalorimeter (MMC) that is configured as a sensitive thermometer for a detector tower, the main experiment. Under single-stage temperature control on the temperature of the mixing chamber plate only with the RuO2 thermometer, the MMC recorded temperature stability of the detector plate of 9 μK rms over 100 min. Under two-stage temperature control, with the first-stage of the mixing chamber plate at 11 mK via the RuO2 thermometer and the second-stage of the detector plate at 12 mK via the MMC, the MMC recorded a temperature stability of 0.5 μK rms over 100 min. Moreover, the heat channels of the AMoRE experiment obtained considerable improvement in energy resolutions when switching from single-stage (RuO2) to two-stage (RuO2 + MMC) control.