Biohazard

If the battery got warmer than you would expect being under the hood with the engine running, it's definitely overcharging. Put a volt meter on it with the engine idling and see what the voltage is. If it's more than about 14.5 or 14.6, it's overcharging and will kill the battery by overheating and boiling away the electrolyte (acid), all over that shiny underhood paint...