An apparatus controlling charging and discharging a rechargeable power storage device mounted in a vehicle, comprising: means (6, 16) for obtaining actual power storage temperature (Tb) representing an actual value of a temperature of said rechargeable power storage device; means for obtaining outside air temperature (Tout) representing a temperature outside said vehicle; means (5, 6) for obtaining estimated power storage temperature (#Tb) based on said outside air temperature obtained by said means (6, 18) for obtaining outside air temperature, said estimated power storage temperature representing an estimated value of a temperature that said rechargeable power storage device has when an ignition-on command (IGON) is received to restart a vehicular system, said means for obtaining estimated power storage temperature including an estimated power storage temperature map having values of said estimated power storage temperature. (#Tb) stored therein in association with a first parameter being said outside air temperature (Tout) and a second. parameter including at least one of: a time zone in which an ignition-off command (IGOFF) is previously received; actual power storage temperature (Tb) obtained when said ignition-off command (IGOFF) is received; and a period of duration for which said vehicular system is active; and means for learning, updating a value of a corresponding value of said estimated power storage temperature in said estimated power storage temperature map, as based on an error between said estimated power storage temperature (#Tb) previously obtained by said means (5, 6) for obtaining estimated power storage temperature and said actual power storage temperature (Tb) obtained when said ignition-on command is received. means (6, 16) for obtaining actual power storage temperature (Tb) representing an actual value of a temperature of said rechargeable power storage device; means for obtaining outside air temperature (Tout) representing a temperature outside said vehicle; means (5, 6) for obtaining estimated power storage temperature (#Tb) based on said outside air temperature obtained by said means (6, 18) for obtaining outside air temperature, said estimated power storage temperature representing an estimated value of a temperature that said rechargeable power storage device has when an ignition-on command (IGON) is received to restart a vehicular system, said means for obtaining estimated power storage temperature including an estimated power storage temperature map having values of said estimated power storage temperature. (#Tb) stored therein in association with a first parameter being said outside air temperature (Tout) and a second. parameter including at least one of: a time zone in which an ignition-off command (IGOFF) is previously received; actual power storage temperature (Tb) obtained when said ignition-off command (IGOFF) is received; and a period of duration for which said vehicular system is active; and means for learning, updating a value of a corresponding value of said estimated power storage temperature in said estimated power storage temperature map, as based on an error between said estimated power storage temperature (#Tb) previously obtained by said means (5, 6) for obtaining estimated power storage temperature and said actual power storage temperature (Tb) obtained when said ignition-on command is received.