Engine Temp indicates in acceptable range, but am unable to touch the engine, radiator area because it is so hot. I suspect the auxilary fans are not operating. Where should I look for a problem and a fix.

Instrument cluster ,it's not really running hot . Did you use an LCD Infrared Thermometer, Laser Sighting: Dual, -58° to 1472° Temp. Range to see actual temp of the engine , hook up a scan tool that can view coolant temp sensor data . What does it show engine temp is , does the PCM - engine computer energize the cooling fan ? Your best bet , take it to a qualified repair shop .

Could be temperature sensor if car is not overheating.
make sure your coolant level is good.
Just to make sure you know this. The radiator fan is activated by the coolant temp in engine. The radiator fan can come on even if the car is turned off.
Something I would check first. Look at the radiator fans. If you have 2 one will come on and off with the A/C. The other will come on when the engine gets to operating temperature. As long as the engine temp is in normal range the engine fan should stay on. When temp seems to rise above normal make sure the fan is running.
I had a issue years ago where the fan relay would get very hot(hot compared to the other relays) and would open and the fan would go off. When the relay cooled down it would close and the fan would run again. I fixed by changing the relay.

Check to make sure both of the electric fans are working. Your car has two cooling fans. As the engine begins to warm up one of the fans will come on. When the engine gets near or above normal temp the other fan will cut on. When you are driving, there is enough air moving through the radiator to keep the engine within normal range. When the car is stopped the fans are needed to draw enough air through the radiator. When the engine is hot and running, open the hood and look to see if both fans are turning. Keep your hands away. Just look don't touch. If neither fan is spinning, or if only one is spinning, you probably need to install a new fan assembly. But check for blown fuses or relays. Have someone check to make sure power is being sent to the fans when they should be spinning.

It is possible, how ever, I would check for inop coolant fan, or restricted radiator. If parts of the radiator are cool to the touch when the coolant fan has kicked in, very possibly resricted flow of coolant through the radiator.

Follow the wiring back from the fan motor, the relay is often found at about the height of the bottom of the radiator on the inner fender. Check that connection is clean and free of corrosion. Check that the fan works by taking two trailing wires directly from the bettery terminals and connecting then to the fan motor directly. Use a voltmeter and check the voltage at the relay when engine is cold and shortly after the radiator top hose from the engine becomes hot (the coolant sensor should have signalled for the fan to switch on at this time). No voltage indicates a break in the circuit or faulty sensor. Voltage but no fan indicates faulty relay

over heating while stopped usually indicates that the radiator fan is not coming on ...when the engine is running hot you should be able to hear the fan running .. if it doesnt then suspect the thermal switch mounted on the radiator .. make sure the fan turns freely .. the fan is not needed when the car is moving so it wont heat up as long as you are driving .. but will do so when stopped if thats the trouble .. sometimes the thermal switch operates a relay that in turn operates the fan ..that could also cause the trouble ..

Sounds like a sticking thermostat (temp up/down).
In an emergency, you can remove it, but replace it soon.

I otherwise suspect the radiator fan, but it shouldn't overheat if you are on a highway going faster than 50mph (enough air blows through the engine compartment).

Everything else you describe does not indicate any other solution.

I suppose it could be the radiator fan RELAY SWITCH or loose wire to it.

Hope this helps....

Likely the fan(s) not turning on when engine gets hot. Is the check engine light on? Read the code(s) and repair as needed. Check (when cold) the fan(s) for free turning--if seem bound or hard to turn, replace the ailing fan. Check the radiator and reservoir fluid level. Watch the fans as the engine heats up. Feel the radiator area where the upper engine hose connects. It will suddenly turn hot when the thermostat opens. The fan assembly should activate somewhat after. Hopefully, the engine code recognized a defective temp sensor and was replaced.

Top up the coolant and verify the sensor is working correctly.

The electric fans on some vehicles dont stay on all the time. If the radiator is not burningyou then i would suspect the guage is bad. The engine would throw a code if the fan was not working properly, so im pretty sure that your fan is working properly. I hope that helps you out.