I have an 87 XJ that had major overheating problems when I bought it over 2 years ago.
I replaced the radiator which was 80% blocked, replaced the plastic bottle and cap which were no longer holding pressure, replaced ALL the coolant hoses including the heater core hoses, radiator hose..., changed the antifreeze, used distilled water with the antifreeze, 50/50 mix, replaced the fan clutch which was shot, I did do any elaborate burping of the system, installed a generic Autozone, 165 F thermostat, and then I simply left the cap off the plastic bottle (burped) and added coolant as the coolant level in the bottle dropped. Once the level stablized I put the cap on the bottle and spend the rest of last two years chasing another gremlin that turned out to be a bad TPS, that tested as good. That was 2 years ago, and I have not had a single cooling problem with it. I did install the aftermarket 3 row heavy duty copper/brass radiator since it was only like $120. (
www.radiatorbarn.com I think?) I did not modify the thermostat on mine.
The 87 Renix XJs have an electric cooling fan operated by a thermal switch on the cool side, return side (drivers side) of the radiator that should turn the electric fan on when the coolant on the cool side reaches about 185 F (+/- 2 degrees F), and the cut off is about 165 F. Mine reads those temperatures on the cool side of the radiator turning the elelcltric fan on at 185 and back off at 165 F when the engine coolant at the thermostat hits and reads about 210 F.
Mine has yet to get over 215 F on a 100 degree day in Houston with the A/C running. I do not tow stuff or hit steep mountains, or really offroad in situations that cause aditional heating of the engine and transmission.
Some other things can cause a properly working cooling system to overheat or when combined can add to an overheating problem. They include a partial exhaust system blockage, lean air / fuel ratio operation, head gasket leak which can be coolant leaking into the exhaust thus the cooling system looses pressure at first allowing it to overheat and finally boil, or exhaust leaking into the coolant thus causing the pressure to rise, and an overheating transmission (T fluid...slipping transmission, oveloaded transmisson towing, burned T fluid from prior T abuse....etc) which is also cooled by the radiator (there is a small heat exchanger built into the cooler side of the radiator that the transmision fluid is pumped though to cool the Tranny fluid, thus heating the coolant), and an improperly charged A/C system can over heat the radiator since the excess heat from the condenser in an improperly charged A/C system is dumped out in front of the radiator.
Even new parts can be defective, expecially fan clutches. A leak anywhere in the cooling system even new parts, can cause it to overheat.
Also not on your list a slipping, just loose enough belt that keeps the water pump and fan clutch from running at peak RPM. This may not be a typical jeep problem due to the serpentine belt, but can be issue in other vehicles so I am listing it here for tha sake of completeness.
Now some of the items I listed above can be discussed in further detail, like what could cause an MPI Renix system to run too lean thus overheating the engine, same with the A/C system (but it is easy to isolate, just turn it off/on to see if it is causing the overheating, same with the transmission, just let it idle in park).
I had a 1976 dodge charger, SE, Lean Burn, for 4 years that had to have everything in it at peak operating performance or it would overheat. I learned more about cooling system problems and excess heat sources from that bloody beast than I care to recall. They only built them in 1976, only car, and last car built in the US with out a catalytic converter, but they were too tempermental about cooling as they aged. It was OK until it hit about 50,000 miles. After that It was constant headache keeping it from overheating. It might have been OK if it had used an electric auxiliary fan, but they were not really using them back in those days, not yet.
What happens if you let it idle with the bottle cap off?
Have they checked the fuel pressure and fuel pressure regulator (related to possibly running to lean) also the O2 sensor can be tested while the engine is running (it controls the A/F ratio)? How well does the engine operate? Also check the EGR valve!!!!
One last question, did they pull the heads, tanks, on the radiator and ROD out the tubes, or just flush it? if they did not Rod it out, it may still be scalled up and partly blocked. Try turning the engine off, and feel the radiator in different spots, or even better get an infrared temperature tester at Harbour Freight for $20 and look for cold spots (no coolant flow). There should be a smooth temperature drop from the passenger side to the drivers side of about 20 to 30 degrees F. My old, bad radiator had spots in the middle of the radiator that were like 110 F while the inlet and the outlet were nearly the same.