had this problem before.
when you start moving again. air flows over the radiator and the engine temp starts to cool.
The problem is the temp sending unit that activates the electronic fan. When the coolant gets too hot it triggers the fan to go on. You'll see wires that go from the fan to a unit that screws in near the thermostat housing.
Its either the temp sending unit/sensor. or the fan is dead.
you can test the fan by connecting it to the battery.
I dont know how much the sending unit is.
The jimmy rig i set up, on my beater, was to connect the fan straight to an Accessory fuse. so when the car is on, the fan is always on. with this you may need to change the fan every 100k or so.
Thats what i did with my 92' beater civic. 350k and counting.