V=IR (Voltage = Resistance x Current).
Ergo, V/R = I
Voltage is 12 and the resistance across a wrench is very small - maybe a few thousandths of an ohm. 12 divided by a very small number equals a very high number.
You’re probably looking at a few thousand amps.
Now, a 2000 kcmil aluminum cable is about 1.6" in diameter and by code, we can shove about 600 amps down it. A wrench maybe what…about 250-400kcmils kcmils and we’re shoving a few thousand amps down it.
It’s gonna glow.
I’ve seen a lot of stuff over the years get fused together based on a momentary spark. So a brief chain of bearings gets formed, a spark happens, some of the bearings (esp. near the non-moving terminals) fuse. This shortens the distance so the next momentary chain needs fewer bearings and some of those fuse to the other bearings, etc.
Brief sparks welding things together is part of the beginning of the history of arc welding.
I think I had this all backwards. I thought that high resistance in a conductor meant more heat, and that low resistance in a conducting material meant less heat (while still hot).
Thanks for the explanation 
To be clear, aluminum is a pretty good conductor (not as good as copper, silver, or gold, but better than steel or most other metals). And that’s precisely what the problem is. If it were an insulator, like rubber or air, absolutely nothing would happen. But because it’s so conductive, lots and lots of current flows through it, resulting in lots and lots of power, which means lots and lots of heat.
To look at it another way, a battery wants its terminals to be 12 volts apart. A conductor wants all of its parts to be at exactly the same voltage. Put the two together, then, and something’s going to fail.
I am surprised, though, that what failed was the wrench, not the battery. I would expect the internal resistance of a battery to be significantly higher than that of a fat chunk of metal. And the internals of the battery would probably cause the working materials of the battery to boil (which would probably cause an explosion) before they got red-hot.
But I don’t think you can do that with a car battery. My only cite is my idiot friend from college who tested car batteries by shorting the terminals with a large screwdriver. You’d get a spark, but no welding or distortion of the screwdriver.
In a pinch, a car battery can be used to arc weld steel. I have done it.
It is a bit scary, as the only control you have over the heat of the arc, is the gap you maintain between the rod and the grounded metal. It can get very hot!
Your friend testing car batteries found out that they were severely discharged.
Doing that usually melts the lead terminals. AMHIK!
The wrench was only on for a short duration, roughly 2 sec. Any longer would have been very, very bad.
It’s not as clear-cut as all that…
A zero-resistance wire would dissipate no heat.
An infinite resistance wire would also dissipate no heat.
So, there must be some resistance that maximizes the heat dissipated. It turns out, that resistance is equal to the resistance of the power source. For a 12V battery, that internal resistance might be a few milliOhms, which is (coincidentally) right about the same resistance as a chunk of metal that spans it’s terminals - hence the glowing wrench.
Does anyone make wrenches out of aluminum?
Yes.
Agree with what you said. Except the internal resistance of a typical 12 V car battery at CCA is about 0.01 to 0.02 ohms. Cite : https://eu.industrial.panasonic.com/sites/default/pidseu/files/downloads/files/18-292_vrla_whitepaper_interactive.pdf page 4
OK, so I’m a liar.
10 is not “a few”…