It's the crank sensor!
Join Date: Nov 2007
Location: Central Minnesota
Gotta post your year/engine for best troubleshooting advice. My manual shows P0303 to be a cylinder 3 misfire. Depending on what year your XJ is, you may be suffering the "heat soak" problem. There is a technical service bulletin on it; here you go. I had it on my 99 and this was the fix. Does this match up with your vintage/symptoms?
1803103 - 4.0L ROUGH ENGINE IDLE AFTER RESTART FOLLOWING A HOT SOAK
Date: 09/05/03 (supercedes 1802702 dated 09/06/02)
Model Year(s): 1999-2004
Description: NOTE: This bulletin applies to vehicles equipped with a 4.0L engine. This bulletin involves the installation of a fuel injector insulator sleeve.
Details: Customers may describe a 20 to 30 second rough idle following the restart of a heat soaked engine. This condition may be most noticeable when the engine is restarted following a prior 10 to 20 minute heat soak in hot ambient conditions of approximately 32 C (90ºF) or higher. This condition may be consistent with short city stop-and-go driving trips and can be aggravated by the use of fuel with a high ethanol content. Depending upon various conditions a MIL may occur due to DTC P0303 - Cylinder #3 Misfire.
This condition may be caused by heat from the exhaust manifold that following engine shut down migrates to the area around injector #3 and causes fuel vapor to form within the injector. This in turn may cause a momentary misfire of cylinder #3 until the fuel vapor is cleared of injector #3. The insulator sleeve lowers the injector #3 temperature to a point below which the fuel will not normally vaporize.
If vehicle exhibits a rough idle, and if a misfire of cylinder #3 is observed following a 10 to 20 minute hot soak, perform the Repair Procedure.
56028371AA Ignition Wire Shield
1. Cut insulator sleeve, p/n 56028371AA, to make two (2) insulator sleeves about 25-30 mm (1 in.) in length. See diagram.
2. Install one sleeve around injector #3, with the slit on the upward facing side of the injector. Install the other sleeve with the slit on the downward facing side of the injector.
3. Confirm sleeve is flush to intake manifold surface around injector.
4. Check injector #3 wire and ensure that the injector is rotated to a 2 o'clock position.
TSB for the cold start rough idle and P0303 code: TSB 18-010-01
99 Cherokee, 4.0 AW4, NP242
Past Jeeps: 49 Willys, 81 Scrambler, 88 Comanche
Without "data", all you have is an opinion!