If you go through the regulator, the heater power required will be added to the existing load on the regulator and could lead to you either, having to disconnect other devices you want to use to stay under the regulator's limit or, worse, exceed the capacity of the regulator fuse all together, requiring, usually, inconvenient replacement.

What you need to consider from the outset though, is the heater's peak maximum power(Pmax) requirement and its nominal operating power(Pwr) requirements and compare these to your regulator's available output capacity in Watts(W), AFTER everything else you want to run is connected and powered on(on paper - a power audit in other words). To stay warm, you may not be able to make a cup of tea at the same time, sort of thing.

If you go the battery direct route, put a fuse on the positive rail/wire to prevent overload. I can't remember the exact formula to work this out, but its part of Ohm's Law and there are a gazillion websites where you put in the information you have and it will give you the answer.

My preferred option would be battery direct, for a couple of reasons.

If you want to pursue it further, feel free to DM me. 

Cheers

Murray