I had a 16' hellcat for a couple years and I just traded it for a '21 hellcat charger redeye with 7800 miles. I noticed today that the coolant temps run higher and the fan kicks on more often. I notice way more jumping around on the Guage. Is this typical on the redeye? Do they just run hotter?
Possibly normal. RE has 797hp vs. 707hp for the Hellcat.
While you are (probably) not asking the RE engine for all its power underway there is more HP being made and thus more heat. (But maybe "stuck" with the Hellcat cooling system which accounts for the "jumping" around of the gauge.)
As long as the coolant temperature remains reasonable, and even under the most severe operating conditions the temperature at some point goes no higher, I don't think there is anything to worry about.
(Years ago when driving in 116F ambient temperature the coolant temperature climbed to 226F. This was quite a bit higher than I had seen it get up to before. At 212F the fan came on running at low speed. At 216F the fan speed was switched to high. I don't think I ever saw the coolant temperature get to 220F. At any rate while the coolant was at 226F it never went any higher. And the cooling system manifesting no signs of any issues. No leaks. No odor of antifreeze.)
While under some situations (prolonged driving in town) my 2018 Hellcat coolant temperature would climb but the fans came on at IIRC 216F and lowered the temperature and shut off IIRC at 208F. After a bit more driving the coolant temperature would climb and the process would repeat as long as I continued to drive the car in town. Occasionally in very hot weather the coolant temperature would continue to go up but at some point the fan speed would be increased and then the temperature would drop.
The car is used. So you want to be sure the coolant level is good. Not too low but don't overfill it either. You want to be sure the coolant level doesn't go down over time. IOWs the cooling system must be leak free.