How many miles on the Edge? Mostly hwy, city, or combo ...? AC actually helps cool down the temp because it causes the fan to kick on earlier than usual and stay on. Remaining on a short while after engine off is normal if the temp warrants that the fans remain on (over 210F or somewhere in that vicinity).
Did you replace the fan controller also, or reuse the OEM controller? What brand did you replace with, and is the connection tight?
I know temps rise pretty quickly while idling for any period of time once the TStat opens on mine, but I have not changed the TStat (still original). Once I get moving, temps come back down fairly quick, though not as quickly as they rose. I think that is normal, but I could be wrong. Keep checking the coolant periodically to see if it goes down too quickly, and/or you start seeing contaminants of any sort. THAT could be a major issue in the making.