abhishek, it is not uncommon for the iPod to heat up while charging. The "poor Battery" may be your problem. I would change the battery iPhone Gen 1 Replacement Battery and see if that makes a difference. The instructions are here. Good Luck.
We have a chance to guarantee our right to repair electronic
equipment—like smartphones, computers, and even farm equipment. This is a once-in-a-generation
chance to protect local repair jobs—the corner mom-and-pop repair shops that
keep getting squeezed out by manufacturers.
Join the cause and tell your state representative to support Right to Repair. Tell them you believe repair should be fair, affordable, and accessible. Stand up for your right to repair!