Arduino UNO R3 has an onboard regulator so you should be able to connect 12V battery direct to the "7 to 12V DC" input jack - just make sure that the positive pin on the board connects to the positive terminal on the battery and vice versa.
You will need some kind of external switching device to control the heating element as Arduino outputs cannot supply that amount of power. You can use a power transistor, a MOSFET or a relay. There are lots of projects like this online so search "Arduino heater LM35" for different solutions.