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When does the car goes in open vs closed mode?
And what could be wrong if the car runs great when you just started it after a night in the garage, but when it gets hot it runs much worse, power loss? False knocks? Bad MAP censor?
Upon start up ECM will go closed loop when the following all have occured:
1) a preset amount of time has elapsed
2) coolant temp reaches prescribed level
3) the O2 sensor is responding properly
It will then go into open loop (reading but ignoring O2 sensor data) when it senses the WOT condition.
When you first start up the engine is cold and you have a rich condition. Mine also has most power under this condition.
To reduce knock by lower engine temp, proper octane fuel, correct ignition timing.
I believe that a failed MAP, like a failed MAF, should throw a code. Though when my MAF failed it didn't throw a code the engine just wouldn't run.
Generally a bad cat won't show up until it's hot as you described. I have run into bad cats. many many times, and the cars all acted just like you have desribed. Just an educated guess though :)