I offer this information in case it helps someone else who searches on these symptoms and has this problem.

The check engine light (CEL) lit on my wife's 1996 2.4L Cavalier (91k mi) but I let it go for several weeks because the car seemed to be running OK at first. Eventually the car began to hesitate and nearly stall when accelerating from a stop. But it only exhibited this behavior once it got warmed up. When the car was not warmed up, it would accelerate fine from a stop.

I took it into a repair shop. (Based on past experience, I think this shop is good and honest.) They said that the computer threw an error at the O2 sensor but they didn't think that the O2 sensor was the problem. I'm a bit confused about that because on the repair invoice it says that they found code "P0125 Fuel Control Coolent Temp", and "P0172 Bank 1 Too Rich".

Upon further investigation, they found a broken vacuum line ($3.50) going to the Manifold Absolute Pressure ("MAP") sensor (which they thought was the main problem). They thought that this was causing an erroneous MAP-sensor reading which was causing the computer to make the fuel mixture too rich. So they replaced the MAP sensor vacuum line. (It's about 4 inches long and 3/8" in diameter.) They also found that the coolant temp sensor ($16.50) was testing out of range and reading at least 100 degrees too cold. They weren't 100% sure if the coolant temp sensor was contributing to the problem but they said that it's worth replacing because the sensor is cheap to replace and it provides important information which the car's computer uses to adjust the richness of the fuel mixture. (If the computer thought that the engine was colder than it really was, the computer would make the fuel richer.) Apparently, one or both of those problems was causing the computer to make the fuel mixture too rich. (Effectively turning on the "choke" for you fellow old-timers.) A rich fuel mixture isn't a problem when the engine is cold, but it is a problem when the engine is warm, which explains why we only saw the problem when the car was warm.

The car works great now.

They charged me for 1:40 in labor (at $90/hour here in expensive Silicon Valley). I imagine most of the labor involved diagnosing the problem and then warming it up and test-driving it. So if you're a do-it-yourself person who is having the same problem (especially if your car is throwing the same codes) you may find it worthwhile to risk replacing the cheap MAP sensor vacuum line (especially if it's cracked at the connection point) and maybe replace the coolant temp sensor.

The MAP sensor vacuum tube is black, about 3/8" in diameter, and about 4" long (though it's curved). It's located at the top of the manifold and connected to the MAP sensor. It's just a few inches behind the top of the radiator (directly behind the sticker that says, "Use Dex Cool Coolant Only"). It's easy to reach and appears to simply push-on at both ends. Instructions on how to replace the MAP sensor and the coolant temp sensor are in the Chilton's Guide.