When started idels high about 2000 rpm then drops when hot cold ?

not told hot or cold engine
the controls for idle are not the same , those 2 modes.
how high is high RPM,.
hot is 800 RPM regulated by PCM + isc idle valve.
cold is controlled by IAC,thermal air control valve.
and runs about 1200 to 2000 rpm,cold
cold in Florida is 1200 cold in ALASKA is 2000.
if the thermostat is bad, stuck open, and 150f coolant temp the RPM will be stuck high all the time
as will huge vacuum air leaks, the MAP sensor sees that and engine screams.
pully connectors is useless as doing so puts he PCM in limp home mode and idle controls are disabled in that mode. limp
there are lots more tests, to do. but my fingers are tired.
get shop to fix it?

THE ECU CONTROLS RPM ALL THE TIME,. HOT AND COLD
ON OLDER ENGINES THERE WAS AN AIR VAVLE
CALLED IAC. (pure thermal, not electric ISC)
IDLE AIR CONTROLLER THAT ADDS AIR COLD FOR HIGH RPM.
no engine told at all so there can only be an generic answer
to work on any car, learn what you have and tell it first.
or post the VIN and I tell you. what is there.
I have lots of old suzuki manuals. from long ago. but parked on my server.
800rpm hot, engine, with head lamps and blower on same time
or shifting from park to drive and RPM is 800RPM and does not drop shifted to drive, if this stays 800 the ISC valve is working
if hot RPM fails , cold has no chance, see????
engines possible

• H25/27 v7
• J20, DOHC, 2.0l gas.
• G16b, 1.6L, ,

all 4 are MAF based fuel injected not MAP vacuum based at all.
on all 4, if vacuum leaks happen engine slows from super lean mix.

if ISA or IAC leaks or stuck open yes RPM too high yes.
yes both love to stick. from 1988 to 2010 about.
today's cars are not the the same, they are TBW throttle by wire, using 1 throttle motor.
tech talk? high RPM is caused by too much metered air.!
all 4 engine run MAF metered air.

again no VIN no joy, the blind guys can not see under your hood.
sorry. (sad face)

the 4.0L engine?
is this engine cold or hot.
why is 2000 rpm wrong for 60mph., (depends on engine and axle size and what gear you were in , then)

the idle speed for hot is too high
did you scan the PCM yet?
if hot , idle is high, is the thermostat holding water temp 180f or above. ? if not that is the problem.

throttle position sensor TPS is sensative to moisture.

0 when it is turned off is normal

Does it rev high when started cold or hot? If it does it either hot or cold, check the throttle position sensor on throttle body. If that is not bad, then check the automatic choke sensor.

it will idle high with air con on and revs will go up and down try turning air con off it that fixes it then there is no problem

its normal .

Have you tried cleaning out the throttle body and injectors with a cleaner?