Big piece of thin, light metal came off bottom of car...

Yes, a heat shield. Probably not much fire risk unless you park in tall grass- that is the primary danger.

It also keeps keep the heat inside your catalytic converter for best emissions reduction. Puddle splash can cool them out of their operating range.

You should reattach it or replace it. Any mechanic can do that, no toyota dealer required- it's just a question of getting under there.

 

You probably won't be able to re-attach that piece in the manner it was originally attached. The little tabs will have torn off. But what you should understand is that it doesn't much matter how it is held on. This is literally the kind of situation you would use bailing wire to fix.

The heat shield needs to cover the catalyst, and it needs to be held on tight enough that it won't rattle (it will try) or fall off easily again.

Sometimes you can use large hose clamps, but honestly a bit of galvanized wire would be ideal. It will handle the heat and the elements, and you just twist it as tight as it needs to be to prevent rattles.

You can pay any mechanic to do it and they may not charge anything beyond labor.

The primary difficulty in actually doing it is access. If you can safely get under the car with enough room to work, you're set.

It might be the only thing on the car repairable with Flintstones technology. Why pay for Jetsons?