Yes, they all seem to come with a "cigarette lighter" plug to connect to a 12V DC source. That plug could be cut off and replaced with some other form of plug to connect to a 12V DC source, but the controller might be relying on a fuse in the "cigarette lighter" plug for over-current protection. Hopefully not, but that is worth investigating.
The question is - how much "power" are you going to need? Both measured as amps (A) to be drawn and, if you are going to use a battery to supply it, the total amp x hours (AHr) to be supplied.
A couple of small heater straps won't draw many A. See:-
http://www.dew-not.com/specifications.htm
The small ones typically draw no more than 0.5A at full blast.
So let's allow for a total current draw of 2A. Work out what yours will be. Playing safe would be to work out your maximum likely, then double it!
Most people would use a small sealed lead acid rechargeable battery, such as this 7.2Ahr one sold by Jaycar:-
http://www.jaycar.com.au/productView...T&SUBCATID=250
You'll need a charger for it:-
http://www.jaycar.com.au/productView...T&SUBCATID=250
And you will need a cable to connect it to the cigarette lighter plug:-
http://www.jaycar.com.au/productView...r&form=KEYWORD
You didn't think of all these extras, did you - this hobby is like that! Sigh!
You''l probably get a good 5-7 hours power from that battery running a couple of small heater straps at 1/2 to 3/4 power.
But you want to draw power from mains 240V AC? You need a power supply, mains operated, 12V DC out. In that case, you forget about AHr and concentrate on the A that the power supply can deliver.
There are neat ones that have a cigarette lighter socket already and supply more than enough power for your needs. Eg:-
http://www.jaycar.com.au/productView...T&SUBCATID=381
BUT, you should be careful not to let it get wet outside - try to cover it with a box to keep dew off it.