Overheating Problem

New problem issue popped up today. Was driving home from work with A/C on - (1st time in a while as does not get too hot here). Had been driving for about 20-25 minutes at
freeway speeds (little or no hills) when I happened to glance down at the temp gage -- it was within millimeters of hitting the red overheat mark. Screamed a few expletives as I pulled to the right shoulder. Turned the A/C off and the heater on and heat gage started to lower. Drove almost all the way home before I decided to run a second test by turning the A/C back on -- sure enough the gage started to climb again. When I pulled into the driveway, I popped the hood (with A/C and engine still on) and noticed that neither electric fan was operating. Turned A/C and car off and decided I will address tomorrow. But curiosity got the best of me and about 1 hour later I went back into diagnose mode. When I turned on the ignition (engine not started yet), the fan (I don't know which one) went into high speed mode for about two seconds and then shut off. With engine and A/C both on, no fan movement by either fan.

Is one or both of these fans supposed to be on at all times with the A/C on?

What do you make of the short fiery "bust" of the fan(s) when I turned the key to "ON" after an hour?

Any help would be appreciated.

For now, I will just not use the A/C and just "Sweat it out"!

Thanks