The DS18B20 is for measuring the environment temperature (not for furnaces or so).
You need a pull-up resistor, the pictures show how:http://fritzing.org/projects/arduino-and-ds18b20-temperature-sensore/http://bildr.org/2011/07/ds18b20-arduino/
You have to install the OneWire library and learn how to use it.
A simpler (but less accurate) solution is the LM35 or TMP36 temperature sensor.
This is a tutorial, http://learn.adafruit.com/tmp36-temperature-sensor
But if the 5V of the Arduino changes, the temperature becomes more inaccurate.
If you use 9V for the Arduino, you can assume the 5V on the Arduino board is good, so the LM35 or TMP36 can be used.
If you use the USB to power the Arduino, the 5V could change.
For a heater, I suggest to use an relay.
How much is the current for the heater ?
To activate the relay you could use a transistor or darlington transistor.http://www.pighixxx.com/abc-arduino-basic-connections/
"Card3" shows how to connect a relay with a BC337 transistor.
Click on "Set 1 (Card 1,2,3)" to open the pdf.
I'm curious about the battery. What kind of battery is it ?