I think I just bricked my Arduino. Any ideas how?
See my answer here. A 12V battery doesn't necessarily provide you with 12V any more than a 1.5V battery provides 1.5V.

See here for example. A 12V lead-acid battery may well provide 12.7V which is out of spec for the Uno.

See the page about the Uno.

You have too much voltage going into the voltage regulator, it tries to dissipate it, it gets hot and either shuts down or fails.

I suggested in the answer above to use a buck converter to down-convert the voltage, and my answer (which was accepted) said that "it is working like butter".