Engine overheats suddenly and rapidly

When I am driving around the neighborhood (outside air temp: 90 degrees), the engine temperature sometimes rises suddenly and rapidly, about 10 or 20 minutes after ignition. But if I slow down or stop or turn or shift into parking gear, the temperature goes down as quickly as it went up. If I keep driving for a few minutes, the temperature may go up again. Sometimes it stays high for an extended period of time and approaches the red mark, so I have to stop the car and turn off the engine and let it cool. Why is it overheating?

I tested the thermostat. It appears to be functional.
The water pump appears to be good.
There are no apparent leaks.
When it overheats for some time, the overflow reservoir fills past the "full" line and the coolant inside boils.
There are no visible problems with the hoses.
The fan works fine.

My latest theory is that there is blockage somewhere in the radiator. I flushed the system several times, got some dirt out, but this does not fix the problem. Is the problem radiator blockage? And if so, is there anyway to fix it cheaply or do I have to buy a new radiator?

Thank you in advance for your help.