Try cleaning the Idle Air Control valve(IAC), it sounds as if it could
be stuck.
To do that, remove the air hose from the throttle body opening,
looking into the openning you will see a "squarish" hole on the bottom
front of the throttle body. With the engine off, spray Throttle Body
or fuel injector cleaner into that opennig(DO NOT USE carburator
cleaner- make sure it says on the can that it is safe for oxygen
sensors) let it sit awhile and soak, if you can get access to the IAC
electrical connector you could exercise it while the valve ia
soaking(I do it by removing the connector, and providing 12v to the 2
pins, but my car is a '97- I don't know the 2001) and than start the
engine. you might as well clean the throttle dody cavity while you are
at it, especially where the throttle valve makes contact with the
body. you may have to repeat it a few times.
HTH
JerryR

Yeah, Toyota's idle air control valve has been having problems beyond
the 99 described in the following article. It's the worst IAC I've
seen. To the point where Toyota will give away the part but charge an
arm and a leg to install. New parts reportedly are as bad as the old.

Fortunately this can be removed and cleaned. Just google Toyota IAC
cleaning.

http://www.autosafety.org/article.php?did=972&scid=10