Disclosed are charging algorithms implementable in an external charger for controlling the charging of both an external battery in the external charger and an implant battery in an implantable medical device. Because full-powered simultaneous charging of both batteries can generate excessive heat in the external charger, the various charging algorithms are designed to ensure that both batteries are ultimately charged, but in a manner considerate of heat generation. In some embodiments, the charging algorithms prevent simultaneous charging of both batteries by arbitrating which battery is given charging precedence at a given point in time. In other embodiments, the charging algorithms allow for simultaneous charging of both batteries, but with at least one of the batteries being only weakly charged at low power levels. In other embodiments, the temperature generated in the external charger is monitored and used to control the charging algorithm. In these embodiments, if a safe temperature is exceeded, then the charging algorithms change to new temperature-reducing schemes which still allow for both batteries to be ultimately charged.