Could be thermostat was the problem, you fixed that but now have air in the system. Burp the cooling system.
When cold take off radiator cap, let car idle for 20 min, put heat on high with fan on medium. Gradually move RPM to 2500, hold for a minute, slowly lower, do this 5 times. Turn car off leave cap off check back in 30 min, if coolant is lower than when you started, then air came out. Top off and put cap back on.
Fan is bad, if mechanical is slipping somehow, if electric then fan is bad, relay is bad or engine temp sensor not sending correct signal so does not come on until is too hot, then cuts off too soon.
When doing the idle test you should hear the fan come on at some point.
What's the year make model of car and miles on the odometer? Is the electric radiator cooling fans switching on when the dash temperature reaches 212 degrees?
Take it to a ca mechanic
Since the problem seemed to ease when you replaced the stat and coolant, I'd guess you still have some blockage in the radiator -- sludge and sediment like to accumulate at the bottom of the radiator and also to clog some of the tubes. If you can rig an adaptor to pump water from a garden hose through the radiator tank, from bottom to top and also from top to bottom, you may flush out a lot of gunge. If you're careful, you can catch and reuse the new coolant in your system. If this is too much for you, take it to a radiator shop for a pressure cleaning.
It's possible, of course, that your electric radiator fan isn't coming on -- in this situation, the wind pressure would force air through the radiator when at speed, and the radiator wouldn't be very efficient at idle.
My car was running hot all the time, but never overheated. So I flushed the coolant and changed the thermostat which solved it. A day later, I went through the drive thru today and it's running warm at idle, but goes back to normal temp as soon as I start driving? I revved the engine while it was warm and it didn't seem to cool it down.
