What is interesting is that heat is localised and is present only for a very short time (sort of induction cooker).
Be very careful with the car battery and use a battery in perfect condition - I would suggest to use a battery charger (choose one which is fused) instead.
Do the experiment outside the house where air is circulating and wear arc welding goggles and filter mask.
A video of the results is here:
Step 1: Hack the AA Battery
You will need pliers and a knife.
Be careful not to break the carbon rod.
Step 2: Carbon Rods
Here you can see one from an AAA battery.
The smaller ones are carbon (graphite) leads from pencils: here you have a 0.5mm and a 0.9mm leads.
Be careful with the smaller leads - they produce a very bright light and you will need arc welding goggles.
Step 3: Sharpen the Carbon Rod
You don't need this step if you are using pencil leads.
Here I am using 2 dremels to do this nicely.
You can use a pencil sharpener although it is more difficult.
Step 4: Lead Solder
Step 5: Jumper Cables
Step 6: If You Are Using Pencil Lead ...
You will need arc welding goggles because of the bright light.
Filter mask is also recommended because of solder fumes.
Step 7: Car Battery
Step 8: You Can Now Solder
I am using pencil rod in this video.