It's normal for chargers and batteries to get warm when charging. For them to get hot, it would suggest something wrong with the battery.
Without part number, pictures or something else to work off of I can't give you any more info than that.
What I can tell you is that a battery for that radio would run you under $40, and would give you the peace of mind that it isn't going to crap out prematurely. OEM (Motorola) batteries are a safe bet, but I've had good luck with the Honeywell brand also, specifically the NiMH 2500mah batteries.
Could be a faulty charger, but that is difficult to ascertain without being able to test it out. If you purchased this stuff used from e-bay or some such site, I'd count on tossing the batteries and starting fresh.