Car runs well when cold, stalls when warm

I own one of Tom and Ray’s favorite makes – a 1989 Peugeot 405 with 150,000 miles. It cranks and idles fine, but lately, as soon as it warms up, it sputters and dies every time I press the clutch and the RPM drops below 2,500 (i.e. slowing for a stop sign.) One mechanic says the whole top end needs to be rebuilt because there’s oil in the cylinders (even though this car has been burning oil for as long as I can remember and I bought it new). Another mechanic says I’ve got an air leak somewhere in the vacuum system, but I tried the old “spray carburetor cleaner everywhere to see if you can make the engine rev” trick, which didn’t work either.

Anyone out there have another idea?

Is it a carburetor of fuel injection? If fuel injected (probably) it would sound like the IAC motor (Idle Air Control) is not working or the TPS (Throttle Position Sensor) section that detects when the gas pedal is not pressed, sometimes referred to as the Idle Position Switch or something like that, is not making. The switch lets the computer know that it needs to take control of the Idle through the IAC cause you ain’t touching the gas pedal anymore.

Yes, it’s fuel injected. Thanks for the suggestions. I’ll have those items checked out.