1) where is it getting hot, if its the main chip your doing it wrong, if its the little 3 pin job near the power input, its going to get warm depending on how much current your drawing though it and at what voltage. Its a 5 volt regulator, requires a minimum of 7volts to work correctly, everything above that is wasted as heat. so if you have 12 volts and drawing a couple hundred milliamps, you can get the datasheet for the part and do the math to see that "yea its going to be hot to you". Hot to the chip is also in the datasheet and its usually enough to make you cuss. 2) no, current is drawn not provided, so if you lower the current capability of your supply, and its not current regulated, its going to suck the current from the supply no matter what, always go over a little.the best way to drop heat from the regulator is to drop input voltage when possible, that's why linear regulators suck.
that part has a maximum junction temperature (how hot the insides get) of 150C or 302f, you could almost bake cookies on it and still be OK
Lower power in would help, like 7.5V.The power above that is just dissipated as heat by the regulator.Here's what I use when I bring power from the barrel jack.http://www.dipmicro.com/store/DCA-07510I generally just bring 5V to the equivalent of a power header instead (custom boards), and not use an onboard regulator at all.http://www.dipmicro.com/store/DCA-0520