A working car battery will get warm after normal driving, due to engine heat and carrying a charge load. If your battery gets very hot, though, it may indicate that your charging system has some problems. On a weak battery the alternator may be working harder than normal to keep it charged. This constant charging will cause the battery to heat up. A faulty alternator can also cause the battery to heat up as well. An alternator with a bad voltage regulator can lead to overcharging the battery, and may damage both components.