samsung galaxy s3 gets hot

Does the battery run down quickly? Could be a failing battery. You could try a new one, or borrow one from a friend who also has an S3.
 
Have you checked the battery page to see the specifics of what the battery is doing

Posted via Android Central App with my Samsung Galaxy S5
 
Do this:

Charge up to 100%, then let it drain to 20-30% with normal usage, without charging in between. Then show us:

1. The main Settings>Battery screen.
2. The fullscreen battery graph screen (which shows Awake time and Cell Signal Strength).
3. The Screen category (to see total Screen On time).
4. The Cell Standby category, if present (to see Time Without Signal).