02 Grand Cherokee High RPM start. Cuts out when driving

Are you shure that it isnot overheating?

Check out related help links to troubleshoot these problem:----Click the link below:---Idles Fine but RPM jumps in drive mode? http://technoanswers.blogspot.in/2012/07/idles-fine-but-rpm-jumps-in-drive-mode.html
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http://schematicsdiagram.blogspot.com/2011/12/how-to-adjust-rpm-on-2009-dodge-charger.html
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Engine cuts out at 3000 RPM? http://schematicsdiagram.blogspot.com/2011/12/engine-cuts-out-at-3000-rpm.html

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Cold start problem and vehicle shudder around 2500 to 3500 rpms
http://repairhelpcenter.blogspot.com/2012/10/cold-start-problem-and-vehicle-shudder.html

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High rpm in neutral? Inconsistant high RPM in neutral? http://technoanswers.blogspot.in/2012/02/high-rpm-in-neutral-inconsistant-high.html

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Jetski Sputters and Low RPM? http://whatisbyme.blogspot.in/2012/07/jetski-sputters-and-low-rpm.html

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Fuel Injection Problem And RPM suddenly increases http://whatisbyme.blogspot.in/2012/07/fuel-injection-problem-and-rpm-suddenly.html

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2005 Toyota Highlander: Engine runs hard RPM below 3000? http://whatisbyme.blogspot.in/2012/05/2005-toyota-highlander-engine-runs-hard.html

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Cruise Control stops working, Excessive cranks to start the engine and RPM goes max 2500 http://whoisbyme.blogspot.in/2012/07/cruise-control-stops-workingexcessive.html

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1990 Toyota 4Runner: Engine cuts off when reaches 2000 RPM?

http://whatisbyme.blogspot.in/2012/05/1990-toyota-4runner-engine-cuts-off.html

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1999 Toyota Camry: Erratic stalling and high engine RPM at idle?

http://whatisbyme.blogspot.in/2012/05/1999-toyota-camry-erratic-stalling-and.html

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1995 Toyota LS: Misfire at idle or low RPM http://whatisbyme.blogspot.in/2012/04/1995-toyota-ls-misfire-at-idle-or-low.html

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Lexus RX: Tapping noise under Valve Cover At Low RPM? http://technoanswers.blogspot.in/2012/04/lexus-rx-tapping-noise-under-valve.html

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These will help.
Thanks.

Check out related help links to troubleshoot these problem:----Click the link below:---Idles Fine but RPM jumps in drive mode?http://technoanswers.blogspot.in/2012/07/idles-fine-but-rpm-jumps-in-drive-mode.html
---------Mitsubishi Lancer rpm needle bounces?http://technoanswers.blogspot.in/2012/02/mitsubishi-lancer-rpm-needle-bounces.html
--------How to adjust rpm on 2009 dodge charger SRT8?

http://schematicsdiagram.blogspot.com/2011/12/how-to-adjust-rpm-on-2009-dodge-charger.html
---------
Engine cuts out at 3000 RPM?http://schematicsdiagram.blogspot.com/2011/12/engine-cuts-out-at-3000-rpm.html

---------

Cold start problem and vehicle shudder around 2500 to 3500 rpms
http://repairhelpcenter.blogspot.com/2012/10/cold-start-problem-and-vehicle-shudder.html

---------
High rpm in neutral? Inconsistant high RPM in neutral?http://technoanswers.blogspot.in/2012/02/high-rpm-in-neutral-inconsistant-high.html

-----------
Jetski Sputters and Low RPM? http://whatisbyme.blogspot.in/2012/07/jetski-sputters-and-low-rpm.html

--------
Fuel Injection Problem And RPM suddenly increaseshttp://whatisbyme.blogspot.in/2012/07/fuel-injection-problem-and-rpm-suddenly.html

----------
2005 Toyota Highlander: Engine runs hard RPM below 3000?http://whatisbyme.blogspot.in/2012/05/2005-toyota-highlander-engine-runs-hard.html

---------
1987 Toyota Camry: RPM Drops going Up hills?http://whatisbyme.blogspot.in/2012/05/1987-toyota-camry-rpm-drops-going-up.html

-----------
Cruise Control stops working, Excessive cranks to start the engine and RPM goes max 2500 http://whoisbyme.blogspot.in/2012/07/cruise-control-stops-workingexcessive.html

----------
1990 Toyota 4Runner: Engine cuts off when reaches 2000 RPM?

http://whatisbyme.blogspot.in/2012/05/1990-toyota-4runner-engine-cuts-off.html

------------
1999 Toyota Camry: Erratic stalling and high engine RPM at idle?

http://whatisbyme.blogspot.in/2012/05/1999-toyota-camry-erratic-stalling-and.html

---------
1995 Toyota LS: Misfire at idle or low RPMhttp://whatisbyme.blogspot.in/2012/04/1995-toyota-ls-misfire-at-idle-or-low.html

-----------
Lexus RX: Tapping noise under Valve Cover At Low RPM?http://technoanswers.blogspot.in/2012/04/lexus-rx-tapping-noise-under-valve.html

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These will help.
Thanks.

Because you disconnected the battery you lost the long trim value,you will now have to relearn the idle,start the vehicle idle it to 1500 RPM,hold for a minute,idle should stabilize,turn on A/C let it idle,for a minute,now your done,

your throttle body sensor may be bad. first get a can of spray carb or fuel injection cleaner and spray it in the opening for the intake for the throttle body. this will clear out the carbon build-up. when you crank it it will run shaky but shoiuld clear up within a minute

Most vehicles run at a high RPM for a couple minutes until they are warmed up, and then it should drop down to normal idle speed.

usually rough Idle is not noticable at high ildle. Once it is idles normally try Disconnecting one injector at a time. If the idle stays the same than that cylinder is the culprit. Remove that spark. If it is wet than do a compression test. Should read better than 100lbs of compression.If compression is good take a spark plug and hook it into the end of the plug wire.Lay it across the intake,start the car and watch for spark. If you have spark than you probably have a bad injector. A miss will cause the vehicle to idle high. The computer is trying to keep the car from dieing out. Hope this helps. No spark do a tune up.

Sounds a whole lot like a dirty or malfuncitionig idle air control valve. A coil would generally show up as a miss under load or high rpm, crank sensors generally work or they dont, only sometimes giving you a miss, but that would be all the time at any rpm. Computer, I doubt for too many reasons to list. Could also be related to a bad throttle position sensor or a very slight vacuum leak.

I don 't know if I can solve it, but I had a very similar problem on a 2002 Grd Cherokee Laredo. It ended up being the Throttle Positioning Sensor (TPS). Unfortunately the part alone is about $125 and and total installed cost was about $250. It would idle high at first, then gradually work it self down to a normal idle. Once it was warmed up it it would have an up and down RPM during idling, and several times it stalled out at intersections. There was also a lot of transmission clunking going on when you put it in reverse or drive.
Runs like a dream now. Clunking is gone and idle speed is just right.

I would agree.