Overheating caused by electrical problem?

Howdy guys, new to naxja and I've read through tons of other forums trying to figure out this issue I've been dealing with. Some were very similar but none exactly the same as what I have.
Okay so I have a 2001 xj, around 147,000 miles when I bought it and since then I've rebuilt the tranny and replaced the engine with a newer 4.0. It's always had a hard start, takes a few seconds to turn over and the battery gauge always lowers when cranking. When it starts up its usually a rough start with a bit of rumble. The Rpms sit at around 400 when idling. After a bit of driving and its heated up it sometimes stalls on me at idle, sometimes won't die. Now a lot of the time after its heated up and I turn it off, I go back to start it up and starts real rough and rumbles and doesn't engage at all. Now here's the weird part, I get my buddy to come and he give me a jump and it starts up. So this is why I'm baffled. The alternator is good I know that. The battery isn't dead. The starter is new. I've replaced practically every sensor except the crank sensor, replaced the pcm. One of the previous owners did some electrical work (adding lights and a sound system, which I have disconnected). The airbag light has never turned off, so all that leads me to believe this is an electrical issue.
I'm just wondering if anyone has had any problems like this or heard of something similar. Thanks for any advice.

What does any of that have to do with overheating?

If it starts good with a jump, I'd look first at the battery terminals. Clean the terminals and battery posts good, then re-attach tightly.

Most likely needs a battery. Not being dead means nothing as to the state of the battery and how much amperage or can put. Make sure cables and terminals are good also. The later xjs are sensitive to low voltage when starting and low voltage can wipe the memory making them hard to start and idle rough until they relearn. Just went thru this on my other xj.

Sorry forgot to mention, when it does this the engine feels hotter than normal.

Gotcha. Man sensitive is a good statement! I didn't have any trouble like this from my TJ. Thanks a lot, I'll try a better battery and see what happens.

Trevorthorr said:

Gotcha. Man sensitive is a good statement! I didn't have any trouble like this from my TJ. Thanks a lot, I'll try a better battery and see what happens.

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Check the cables first. They are cheaper than a battery and a new battery won't fix bad cables.

Ya I'm starting with that. Mine are pretty shot.