To get batteries hot, you need to draw plenty of current. I wonder if something is shorting... can you check the pins/connections on the grip, if anything looks like bent or something?
In a sense I was thinking if you'd test with NiMHs instead of alkalines, as they can give even higher current. But there's big risk if something has shorted, as that could damage something even further. So I recommend not to try, but try to find out what's wrong.
Can you check all the ports also if there's any pins bent? For card slot you might not be able to see properly, but does it behave same without a card?