There are a few things here to check one is I might want to flush the coolant system on it especially bec it's a used newly purchased vehicle.Personally I recommend doing this so you know exactly what you're dealing with and then can keep a better eye on the way the engine temperatures get affected and change during the regular operations of the vehicle.
From what you're saying I'd want to know if the fan is engaging one thing you can do is once you know you've flushed or fully tested the anti-freeze with a proper anti-freeze tester is watch and listen for the fan to engage when the vehicle sits idling.If it's not engaging try turning on the A/C on high and see if any fans engage.First possible cause if not engaging is the temperature sensor, or the fan fuse or a fan relay or the fan or the wiring going to any of the mentioned devices in the circuit.One common fault is rust and corrosion and believe me that aged of a vehicle and where it's from etc tells me for sure that vehicle has rust and corrosion issues in it's wiring internally and externally , especially in it's charging system and plug in connectors for the sensors etc.
The basic rule of thumb is if a engine doesn't over heat driving it at hwy speeds then the water pump is probably okay but the pump could have a internal blade that is damaged etc or a leak and thats one reason it might only over heat when idling.
It's also vital that you've the proper thermostat in the engine especially if you live in extreme temperature climates.Another vital thing is the quality and mixture of the coolant and don't use reg water use distilled water if adding water to coolant system and never add cold water or anti-freeze etc to a hot engine.
Most common fault is a fan not engaging when the engine sits idling and it over heats and mostly the relays cause such a problem and keep in mind that on those vehicles I believe the low fan relay is what runs the two relays so if no fan engaging try the low fan relay first.Be sure once you've the engine idling or when you approach it or park it to always check for leaks especially if it's an older used vehicle.
Hope that helps and best of luck.By the way another cause can be a air clog or air bubble or a faulty rad etc or even again a leak so be sure you check it all over fully.If I was you I'd be changing the transmission fluid and filter on it and checking for any factory recalls or service bulletins or flash updates or newly not in owners manual fluid changes or recommendations.
One last little note here if that vehicle has over heated on you or in the past then the transmission also has internally over heated , it's fluid is burnt or worn out and the special chemical additives that dodge uses in it's transmission fluids is also worn out and causing shifting or bucking or stuttering etc issues or will be soon and once you've this over heating issue fixed I'd be changing the fluids in the transmission and doing a full oil change too on it.
