From Experience I can say that there might be a short. Either that or the battery is done. You can replace the battery but a short is irreversible. If the phone is under warranty I suggest you trade it in.
Another thing possible is that the phone is bricked. Does your pc recognise the phone when you plug it in? If it does, then the phone is bricked. If not, then follow the first paragraph.
How to (hopefully) fix a brick:
1. Press and hold the volume up and down keys at the same time.
2. Power on the phone.
3. If that does not work; assume you have either a corrupted nand, or a completely dead phone.
A corrupted nand can only be fixed by flashing the nand. I do not know how to flash a blackberrys nand.
NOTE: A nand is the phones internal memory. It store the firmware of the phone.
You stated that the phone gets hot. Overheating can seriously damage a phone.
Hope this helps!
UPDATE PLS READ FIRST: After some research I figured out the battery is unremoveable so disregard the replacing the battery.