2011 BMW 335i convertible coolant temp issues

[Bigchungis123]

I just recently purchased this vehicle and immediately fell in love with it. I commute 150-200 miles a day in it. It has 140000 miles, no leaks and has been garage kept. I have noticed lately that about an hour into driving or in traffic the engine temp slowly creeps to about 240 almost halfway. Sometime it’s back and fourth to 210–240. I parked it when I got home and opened the hood and notice the cooling fan was on for a second or 2 then shuts off. This morning I turned the heat on and set fan halfway up and notice the coolant temperature starts to go back to normal from 240 down to 200-210. Coolant level is good, water pump test is good. Thoughts are coolant sensor, plug, bad radiator fan, bad plug. Any thoughts