Wife was driving car and the motor died on the street. Towed home. Replaced fuel pump since it seemed the engine was not getting fuel. The engine starts now and runs at normal idle until the engine is at operating temperature. At operating temperature the idle gets slightly rough, pushing on the accelerator seems to drown the engine-it slows down. Sometimes it sounds like a muffled backfire. I've tried this startup four times and always the same result, no problem until the motor is warmed up to normal operating temp. Auto is 2001 LX with 2.0 motor with 56 K miles. No codes. I have measured ambient air temp sensor, coolant sensor, and IAC sensor. All three show within normal resistance . Checked MAF sensor visually. The housing is clean and sensor is shiny with no buildup. What should I check next? Thanks for helping. I have cleaned the EGR valve with carb cleaner-moves freely and resistance values are correct. Measured my vacuum at 18 1/2 inches when cold and at 20 1/2 when engine is warm.
Asking for more suggestions since vacuum is in normal range.

 

After it's warmed up the iac is out of the loop, have you cleaned the egr valve? It could be a cat issue, but with that many miles I doubt it. Clean the egr valve.

 

Maybe the computer doesn't know the engine is warm? The coolant Temperature sensor might be failing. Rare but possible.

My guess is that it is a vacuum leak of sorts. When cold the fuel air mixture is enriched anyway, once warm the fuel air mixture is too lean. Look for disconnected hoses that go to the intake manifold and the tube between the air filter and the intake. Make sure the PCV system is working and sealed.