2002 overheating & misfire code

Hi I'm new to the group. I have an 2002 liberty sport that i purchased recently. Previous owners have repaced the water pump , thermastat, resiviour tank, radiator cap and hoses, as well as the radiator, i removed the bleeder plug and a good bit of air escaped, i then fill till water was coming out and put plug back in. I had previously flushed radiator with prestone flush , following man. directions. It ran well at idle for over trity minutes several times. When i took it for a test drive after about ten minutes the temp guage showed temp increasing oadt half way. And when stopped at red light engine ran rough and was trying to knock off. The rough idle had not been a problem prior to this. Code reader says engime miss fire cylinder 2. Anybody have any suggestions? Im stumpted. Half the time when gauge says overheated checking enge and hise temp wuthnlaser temp gun indicates temps no higher than °255. Other times starts running rough spark knocking, valves rattling. But never is it appeared to b low on coolant, leaking any fluids, or steaming. Plz. Help

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Welcome to the forum.
Misfire # 2 - It may need a new set of 6 spark plugs, jeep likes new plugs. Water getting down coil pack seal #2 may be a problem as well- use compressed air to dry it out.
I would remove that spark plug, make sure it is clean, gapped properly @ 0.040 inch or install a new plug NGK ZFR6F-11G and then move the coil pack over to another cylinder & see if the code jumps to the other cylinder.

Overheating issue, is the electric fan coming when it is getting hot above 227 F ? Test fan by turning on the AC or a defrost position and the fan should be running.
The Jeep requires Hoat coolant or Zerex G05 only. A Mopar thermostat should only be used/installed.

Valve noises not good, address misfire, hopefully you can get it firing properly & then take it from there, see how it's doing then..

Not sure on the misfire but as to the coolant I had an issue where more than one mechanic said it looked like the engine did not get flushed correctly at the manufacturer. When I replaced the radiator it was full of fiber looking crap, like the stuff you find in coolant sealers however I am the original owner and never used such crap. Then when I had the engine replaced the mechanic had me come back by and look at all the paste on the inside of the engine where the coolant would flow. Prior to the radiator pull and flush we think the fiber crap was getting in the water pump and thermostat and restricting coolant flow then it would blow by and cool just fine for awhile.

Considering the crappy heater core used in the Liberty and the cost of replacing I would certainly flush, even pulling the hoses to get a good look and replace with Mopar HOAT. If anything other than coolant came out I'd be pulling the thermostat and backflush the heater core and system as much as possible, even paying for one of those heated coolant flushes some places can do. Of course check to make sure the electric fan is kicking in and the mechanical fan clutch if so equipped.

Supa Dave, I see you attempted to make a reply above.. but no statement from you.
Try again only this time look for the box where it says.. "Write a Reply" .. type in there..then click on copper colored box "post reply"