A roller fixing unit for a color electrophotographic apparatus having a fixing roller and a pressing roller rotating in contact with each other, at least one of the rollers acting as a heating roller, as well as a control unit for connecting a power source to the heating device for only a predicted time duration based on a detected surface temperature of the heating roller so that the surface temperature of the heating roller reaches a setting temperature before the time when the top end of a first sheet of print medium having a color image arrives at the fixing roller in a case where the surface temperature of the heating roller in a standby state is lower than the setting temperature. The control unit is set to perform a power source connection for every sheet of print media coming out from an intermediate transfer unit in the color electrophotographic apparatus.