I have a 88 XJ and in 2000 I replaced the factory radiator, factory fan clutch, factory thermostat, factory heater hoses, factory heater hoses, pressure cap on pressure bottle all the result of a broken fan belt. I figured it was the factory fan belt with 115,000 miles on it.
You have not mentioned anything about the age of your XJ's components. Here some rules of thumb I have picked up over the years:
* Radiators - 7 years max life, anything more is just good luck
* Thermostatic fan clutch - no good way to test them, replace at 5 years of age
* Hoses - replace every 4 years regardless of mileage. Also make sure your lower raditor hoses has a spring inside, it can be sucked shut of the spring is not present and cause overheating. I use dealer radiator hoses, well made and have the anti chafe installed. I also use dealer heater hoses, no aftermarket store lists all 6 sections of heater hose.
* Thermostat and "radiator cap - I change every 4 years when I am changing hoses. I also use ONLY a dealer (Mopar) themostat. ONE overheat can damage both of thse items and I can confirm that.
* coolant - use distilled water to mix with coolant, also flush out the block with distilled. You do not want to add minerals to the cooling system to make your situation worse.
Your profile says you have a 1990 XJ, the plastic pressure bottle known for failing and not holding pressure. You can get a new one for $20 from
www.quadratec.com and that includes the "cap".
It sounds like you to do a cooling system renewal - radiator, fan clutch, thermostat, pressure bottle & cap, and radiator hoses. Also if you do heater hoses, do them if you still have the aluminum bands at the wye ftting and heater control valve. Also if you change the heater hoses you can flush out the heater core.
When you install the new radiator hook back up the trans lines to the radaitor cooler. Your worry about overheating is a little unfounded, there "engineering" that went into sizing that Aux cooler also adding the second cooler will do essentialy nothing more to cool the ATF.
I also hope you have the owner's manual so you know how full to fill that pressure bottle.