It would be useful for us to know if your JK is a short or long wheelbase, what kind of tranny is in it, and what gearing you have. And if an automatic, do you have a transmission cooler.
But even still, I'm not sure anyone can here can give you a definite answer on this, as a lot depends on the circumstances. Things like the terrain your going over, the temperature it happens to be outside, if you happen to get stuck in traffic, and how you tend to drive can all make a difference.
Check your owners manual of both vehicles, the JK to see how much it can tow, and the CJ to verify how to setup the transmission/transfer case/hub locks/steering lock etc. for flat towing.
You could also call your local Jeep dealer and check their opinion.
Check the laws of the states you will be passing through to see if they have any specific requirements (like brake controllers or light wiring.)
My main concern would be more on the braking side of things. Heavier trailers usually have an braking setup. You didn't mention if your CJ would be tied into the JK's brake system, so I'm guessing not. Doubling the weight to be stopped is a lot to ask of the JK brakes. So if it were me, I would probably play it safe and just rent a trailer. (one that gets all 4 wheels off the ground, a 2 wheel dolly can damage 4wd vehicles.) And I would prefer to have have brakes on the trailer and an electric brake controller in the JK. But that's just me. Stay safe man.
How much does your CJ weigh? So many variables. What 2013 Wrangler do you have i.e tranny, gearing, 2 or 4 door. A CJ can be fairly light and flat towing it maybe ok. I would not attempt this if the CJ was on a trailer but if it is light enough and your not using a trailer... I also would not do it if you have a 2 door jeep.
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