It won't hurt it. Your car battery charges while you're using it, doesn't it? Yeah, I know, different battery technologies, but same applies. Most people charge their laptops while using them too. The battery still charges, it just won't charge as quickly, or at the very least it will slow the rate of discharge. Take a GPS app, for instance....if you're going to be using it for any significant length of time you need to have it plugged into the charger, otherwise it's just too much drain on the battery. It will actually make the battery less likely to get too warm because it doesn't have to provide as much current. Where does the extra current come from? The charger.
One exception that I can think of would be if the charge on your battery is very low. You'd probably want to let the battery charge for a while before using it, although the circuitry that monitors the battery should protect it if it's working correctly.