[AC Question]

I have an s3 let installed with a custom rom recently.my phone perfectly charged when it is on but when it is off the red light(led indicator)list showing that it charges but when I click the power button home button or volume buttons the led indicator turns off without showing the battery level and it disconnects from power and do not charge.help me.my battery also heats a bit When using

[smvim]

When you flash a different ROM it's often a good practice to wipe the system cache partition afterwards and since you're rooted while you're in Recovery Mode you might also want to wipe the Dalvik cache.
If you still have charging issues you might want to try re-flashing the ROM. If the same problem persists, not to dissuade you from asking questions here, but with a custom ROM you might be able to get better answers to problems from the developer(s) of that ROM.