I congratulate you on doing regular fluid checks, but that diligence can’t prevent problems like this from taking place as your car ages.
My best guess would be a defective temperature sensor that is not detecting engine warm-up.
If the temperature sensor proves to be okay, then perhaps the Idle Air Control motor (IAC) is to blame. A decent mechanic should be able to figure this out without too much trouble.
A Corolla this age used a cable from the gas petal to the throttle body. The cable could need lubrication, and the linkage at the base of the throttle body could need cleaning and some lubrication also. Start with these simple things and if there is still a problem then get into more troubleshooting.