I always use a 16, but anywhere between 13-16 will work. A 16 raises the boiling point by about 10 degrees or so.

It might be 16 on the newer models. I would use the FSM listed rating and make sure it's a quality part.

The cap and overflow are critical components of the system - yes, they can and will cause overheating issues if they are not working correctly. Regardless, you want to correct any issue you have if for nothing more than eliminating it as a possible root cause.

Not to create a debate but I did some reading on radiator caps and pressure ratings...and basically the higher the pressure rating the higher the boiling point before release into the overflow tank which means the coolant is absorbing more heat from the engine...higher pressure cap = cooler engine. I am certainly no expert and this was counterintuitive to how I would have thought about it but does make some sense....thoughts?

For some reason the earlier XJ's ('95 and back) used 13lb caps (12-16 range). '96 and up 16lb caps (14-18 range). Don't know if all that matters though.

I am wondering if you hear the clutch engage on your engine driven fan? A clutch fan is a terrific way to provide increased air flow thru the radiator......if you do not hear it engage at first cold start, and then any time it starts to even think about heating up, then your clutch is not working properly. This is easy to misdiagnose on an xj because the auxiliary fan will come on and keep it from overheating, but with a good clutch on the engine driven fan, the auxiliary fan will not come on very often, if all other components of the cooling system are in order......experienced this myself on my xj.....amazing improvement with new, high quality clutch.