1999 Saturn SL1 RPMs stay up while moving

I start car, idles fine at about 800 rpm. Push on gas pedal while in netural (5 speed) parked, rpm drops down to 800 right away. Everything is good so far. When driving and shifting between all gears, rpm will go up about 200 rpms more, when clutch pedal is pushed down while car is moving. Also when I roll to a stop coming to a stop sign or in neutral free wheeling down a hill. As long as the vehicle is moving the rpms will stay at about 1500 rpms for about 15-20 seconds, than go down to 800 rpm. As long as I stay parked or not moving rpm works fine, drops down to 800 rpm right away. Service engine light does not come on. Only when moving does the rpm seem to raise some what, maybe something do to with transmission speed sensor if there is such a thing. I replaced The idle air control (IAC) valve and temperature sending unit. And cleaned the throttle body. SI talked to a dealer and Advance Auto parts. I hope this explains it