Overheating 360 at Idle

After going for a 1/2 hour drive through the local hills, car was idling for a couple of minutes, and noticed the temperature going above 250F. I initially thought that this was a fan failure, but the fans would come on, both passenger side and driver side in synch for only about 15 seconds then switch off, not enough to bring the car back down to 250. Also, after switching the car off, the fan do not run like they used to,typically cooling down the engine. Once the car is in motion, the temperature quickly cools down below 250.
The only thing that was recently changed on the car was the Battery.
Note: If I run the AC, it does not engage the fans.
Planning on taking it for its annual over the next couple of weeks, but in the meantime hoping for some feedback as to potential root causes.

 

I had checked it. Initially the level was a little low and filled it back to ~45mm from lower neck (Cold) and still ran into the same overheating issue once the car warmed up.