OK, I tested the cat on a different Toyota yesterday with my new thermometer. I hunted and hunted around the catalytic converter, catalytic converter shield, muffler, exhaust manifold, and everything could think of. The highest recorded temperature was 110 C, and the truck wasn't off for more than 5 minutes before I checked.

I'd have checked mine, except for two reasons: First, I have no catalytic converter. Second, the exhaust manifold gasket blew a couple days ago, so it's not going to the field 'til that gets fixed.