My 2001 XJ has been idling rough but only during cold weather (below 40F). It idles very low as well, 500-600 rpm or so. I did as much research as I could to find the culprit. I replaced the throttle position sensor, Idle air control valve, and ambient air temp sensor. I cleaned the throttle body too.

Nothing has helped, and it's running as rough as ever. For some reason when it warms up it will run fine.

Curious if you guys have any suggestions?

Thanks!

Get an OBD2 scanner so that you can find out what your fuel trims (air/fuel mixture) are doing. Bluetooth scanners can be had on amazon for about $25 (I prefer the BAFX brand, and run Torque Pro from Android play store).

Having this will greatly help you determine if there is a problem with the O2 sensors, temperature sensors, throttle position sensor, etc. It will also show you what the computer thinks is going on regarding RPM, and other data points.

Have you tested your system voltage (running and not running) yet?

If you have a multimeter (and no self-respecting shade tree mechanic should be without one), check the coolant temp sensor. I don't recall the resistance values exactly, but should be fairly high when cold (3-4k I think), and fairly low when hot (under 100ohms).