2000 Toyota Echo Overtemp warning light

Car runs fine at 65-70 mph on the freeway with no overtemp indication until pulling off freeway and stopped at stop light. Overtemp light comes on pull off road and check cooling fan, fan not running. Continue on way at 45mph for about 1 mile and overtemp light goes off. Stop at stop light overtemp light comes on. This sequence of events is repeatable. Not sure of actual temperature but no boiling over or significant coolant loss evident. My first diagnosis was possible intermittent thermostat and/or blocked radiator. Had radiator flushed and thermostat replaced. The shop also said they checked for a blown head gasket. No change. Replaced radiator cap. No change. Repair shop diagnosed blocked radiator. Had radiator replaced. No change. Replaced fan temperature switch. No change. Bypassed fan temperture switch so fan ran continuously. No change. If I run the engine at a fast idle radiator fan will cycle on and off maybe overtemp light will come on maybe not. Seems to be now correlation between radiatior fan and temp warning light. Overtemp light may come on without fan coming on or fan may cycle on and off while overtemp light remains off or with the light on fan may come on and after awhile the overtemp light may or may not go out. No OBD codes are being set. What am I missing? The only relevant things left in the system are the radiator hoses, water pump, the engine coolant sensor, the Engine Control Module, and the hot and cold idiot lights. This car is used for daily commuting to and from work in Phoenix, AZ and with summer coming on the last thing I want to see is an overtemp light when stalle on the freeway in afternoon traffic when it 110+ degrees.