Red triangle plus check engine error lights

I have a classic '02 with about 69,000 miles, and for the first time I got the red triangle (!) + check engine + PS/Battery/Problem error lights and screens today when I started the car. I drove it for a few miles around the neighborhood to see if it would go away. It didn't, but the car seems drive fine, and the Energy screen shows a charged battery and seemingly normal arrows going to and from the battery.

Coincidentally my wife usually doesn't drive the car, but she moved the car in and out of the driveway, maybe about 50 feet back and forth, earlier today. She said she didn't see anything wrong, but when I pressed, she says she also saw some error messages on the MFD like I described, and before she shut down she thinks there was a warning about temperatures being less than "41 degrees".

Now it was one of the frostiest nights this winter for the San Francisco area last night, though probably not colder than right around freezing, and I did have the car outside instead of in the carport. However it must have been over 50 degrees by the time she and I started the car. Could cold weather (relatively speaking for SF) possibly have caused an error code?

We also have a fairly sloped driveway, so it was sitting out last night on a 30 degree slope. Could that plus the cold weather caused some temporary error, for example the car tilting causing battery fluid or oil level being too low in a cold state?

I've read up on past posts and it seems these errors come on and in many cases go away for any number of unknown reasons. So is it correct that if the problem is not persisting, that the errors will reset themselves after a couple of restarts? And if I take it to a dealer and show them the light, it's their obligation and cost to check it under warranty (we have the 7 yr/ 100,000 mile Toyota extended warranty)?

Thanks for any advice. I'm using our other car until I determine whether I should try to keep driving it, or to take it to the dealer right away.

 

Thanks so much for the suggestions, especially the detailed ones from tochatihu, and apologies for not making it back to the board all week to give an update. The people on this board are great, and I'll add my follow up here in case it may be at least trivially useful for others down the road.

As tochatihu mentioned, after you restart about three or more times, the warnings may go away. So that day I'd restarted it twice and panicked when the warnings were still there, even though the car seemed like everything was running normal, but probably should've tried a few more times. The next day I started it again and the red triangle went away, and so I tried restarting it again immediately and then the check engine light was gone. It's been running fine since then. I suspect my wife may have just mis-started the car in some innocuous way that led to the error condition in the first place.

Since I'm due for an oil change soon, I'll take the advice of all of you and have them check out the error codes that may still be in there - as you all have mentioned, the extended warranty is paid for. And I'll be sure to throw out that magical "54" when I do! (But isn't "42" the answer to life, the universe, and everything?)

(To one question, I believe the battery is original with the SSC-40G campaign performed by the previous owner.)