4runner overheating problem

4runner 2000 4 cylinder. radiator cap interior components came apart while driving the car, antifreeze leaked out through the plastic reservoir, the engine overheated and I stoped the car. I refilled with water after cooling down the engine and went home about 4 miles away, but now the engine is overheating, I replaced the radiator cap, replaced the thermostat, flushed the radiator, removed radiator hoses and tryed to flush the engine water jacket with garden hose trying to remove any loosen radiator cap components, put everything back together and still is overheating. No leakes detected. Is it possible that there are radiator cap components and there is a blockage somewhere in the engine.

Should I take the engine apart and look for remaining cap parts?

Tryed by filling up radiator with water all the way to the top and kept the engine idled, did not see any bubbles or air coming out of the radiator, what I noticed is: the car overheats while driving but comes to normal temperature when idle.

Is there a clue here?

Did same thing with and without thermostat.