You will need a car battery, AA battery, Jumper cables and solder. Touching the carbon rod from AA battery with the solder closes the circuit - this produces heat (& light!) that melts the solder.
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
This is a very messy step.
You will need pliers and a knife.
Be careful not to break the carbon rod.
Step 2: Carbon Rods
You will get bigger carbon rods if you use bigger batteries.
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
For greater precision while soldering you will need to 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
Cut a piece of lead solder with pliers.
Step 5: Jumper Cables
Get some jumper cables; Hold the piece of lead solder in one alligator and the carbon rod in the other alligator.
Step 6: If You Are Using Pencil Lead ...
... you will need 2 coins to hold the pencil lead, otherwise it will break in the alligator jaws!
You will need arc welding goggles because of the bright light.
Filter mask is also recommended because of solder fumes.
Step 7: Car Battery
Get a car battery and connect the alligators to the battery terminals.
Step 8: You Can Now Solder
A video is available below.
I am using pencil rod in this video.