A battery system including a vehicle-mounted battery configured to supply power to a rotary electrical machine for traveling and that is rechargeable by external power supplied from an external power source, the battery system comprising: a power detection mechanism configured to detect output power from the external power source in a plug-in state in which the external power source is connected to the vehicle-mounted battery; a charging mechanism (30, 32, 34) configured to charge the vehicle-mounted battery by the external power; a temperature raising mechanism configured to be powered by the vehicle mounted battery and configured to raise a temperature of the vehicle-mounted battery to a temperature not lower than a prescribed reference temperature; and a control unit configured to control the charging mechanism (30, 32, 34) and the temperature raising mechanism, wherein in a low-power state in which the output power detected by the power detection mechanism is lower than a prescribed reference power, the control unit is configured to prohibit a temperature raising process by the temperature raising mechanism when an SOC of the vehicle-mounted battery is lower than a prescribed charge reference value, and to cause the charging mechanism (30, 32, 34) to perform a charging process, wherein the reference power value has a value that enables completion of the charging process within a prescribed time when the charging process and the temperature raising process are performed simultaneously, and wherein in the low-power state, the control unit is configured to cause the charging mechanism (30, 32, 34) to charge the vehicle-mounted battery until the SOC of the vehicle-mounted battery reaches a charge stop value which is higher than the charge reference value, and then if the temperature of the vehicle-mounted battery is lower than the reference temperature, to cause the temperature raising mechanism to start the temperature raising process and wherein, in the low-power state, when the SOC of the vehicle-mounted battery is lowered to a level below the charge reference value during the temperature raising process by the temperature raising mechanism, the control unit is configured to stop the temperature raising process by the temperature raising mechanism, and to cause the charging mechanism (30, 32, 34) to charge the vehicle-mounted battery to the charge stop value. a power detection mechanism configured to detect output power from the external power source in a plug-in state in which the external power source is connected to the vehicle-mounted battery; a charging mechanism (30, 32, 34) configured to charge the vehicle-mounted battery by the external power; a temperature raising mechanism configured to be powered by the vehicle mounted battery and configured to raise a temperature of the vehicle-mounted battery to a temperature not lower than a prescribed reference temperature; and a control unit configured to control the charging mechanism (30, 32, 34) and the temperature raising mechanism, wherein in a low-power state in which the output power detected by the power detection mechanism is lower than a prescribed reference power, the control unit is configured to prohibit a temperature raising process by the temperature raising mechanism when an SOC of the vehicle-mounted battery is lower than a prescribed charge reference value, and to cause the charging mechanism (30, 32, 34) to perform a charging process, wherein the reference power value has a value that enables completion of the charging process within a prescribed time when the charging process and the temperature raising process are performed simultaneously, and wherein in the low-power state, the control unit is configured to cause the charging mechanism (30, 32, 34) to charge the vehicle-mounted battery until the SOC of the vehicle-mounted battery reaches a charge stop value which is higher than the charge reference value, and then if the temperature of the vehicle-mounted battery is lower than the reference temperature, to cause the temperature raising mechanism to start the temperature raising process and wherein, in the low-power state, when the SOC of the vehicle-mounted battery is lowered to a level below the charge reference value during the temperature raising process by the temperature raising mechanism, the control unit is configured to stop the temperature raising process by the temperature raising mechanism, and to cause the charging mechanism (30, 32, 34) to charge the vehicle-mounted battery to the charge stop value.