Temperature gauge 260 degrees into red zone no significant coolant loss

The sub model of this car is SL.As I approach or at around my first mile of driving, the temp gauge needle moves into the 260 degrees red hot zone. I stop car and put in park and turn off engine. I immediately restart engine and needle moves down toward halfway mark at 200 degrees or even slightly below. Then I drive another half mile and the needle moves back toward and into the red hot 260 degrees zone. I again stop car, turn off engine, then restart and the needle moves back toward and to the 200 degrees half way mark on the gauge. This cycle keeps repeating. Importantly, I have my heater at hottest setting, and blowing full blast the entire time the engine is running. I keep left hand on the wheel and right hand over the vent, and I can note and predict the temperature gauge needle movements by the temperature of air blowing on my right hand. (I have always had a good working heater in the past). As the air hitting my right hand turns from hot to relatively cool (I do not have air conditioning), the needle moves up higher and goes into the red zone 260 degrees and the red hot light comes on. I am immediately pulling over in ten or twenty yards to turn off the engine. On some occasions here, before I pull over, the air blowing on my right hand goes from relatively cool to, what it should be, hot and the needle moves back down toward and to the 200 degrees middle mark. I do not see any antifreeze/coolant leak under the hood. Hoses appear intact.There is no antifreeze/coolant dripping from anywhere. There is still antifreeze/coolant in the coolant recovery tank. I have a theory. These described occurrences seem consistent with a pattern where there are some loose, solid or gelatinous gooey pieces of gunk in the antifreeze/coolant liquid that hits "bottlenecks" in the flow system and intermittently, temporarily stops flow, and then this stuff becomes dislodged and flow resumes. Please help. I read that my car has an 11.6 quarts (just under three gallons) coolant in the system including recovery tank. Should I flush out the system, maybe run some garden hose water flow through the system for a while ten or twenty minutes) to flush the system out?
Note: important thermostat and water pump just replaced and fan coming on and recently was replaced, radiator recently replaced
Because of this problem, my mechanic put in a new thermostat and new water pump on 12/24/16. Car was fine for a week now this problem with needle going into the red zone has recurred, and this problem is the same thing that was happening on 12/23/16, pre new thermostat, new water pump placement. Also, in September 2016, my mechanic put in a new radiator (old original radiator was leaking) and put in a new cooling fan. The cooling fans seem to be coming on okay.