Why does my car overheat after getting off the freeway

Today as I ran the car on a trip on the freeway to test if it would overheat (and it did start to heat up past its normal operating temperature), I got back to my house and while sitting in the driveway and starting to heat up well past its normal operating temperature I opened the hood to observe it while it was warming up I noticed that the fan was not running. Isnt this something that should be running while its warming up like this to try and cool the water down? And of course the engine had overfilled the overflow.

Replaced the fan switch today and the relay. Fan working now like its suppose to but obviously only part of the problem. After taking a drive to test the cooling fans, the fans worked good and the car did not heat up as fast but never the less it did heat up again. Again at freeway speeds the car is cool and doesnt heat up. Or if I havent driven on the freeway and just drive it around town the car doesnt heat either. I am boggled and have no idea. Im starting to think that the brand new radiator that I installed which after installing it this all started might be bad. Only things left to replace on the cooling system would be the water pump. Again, any ideas?

I did notice that when I stopped to get the relay that the recovery tank was almost full already, and I only drove about 5 miles or so to the auto parts store.

The fan was working. The temperature reading said that it was at its normal reading. The cap was new, and came with the brand new radiator, so I assume that its the correct fit.

Changed cap today cause I do not have the means to pressure test the cap, and drove it to test it. It did heat up again today and when I got home I decided to let it idle and observe it. It first would heat up about 3/4 the way to the H, then the fan would come on and cool it down to normal operating temperature, and do this a couple times. Then it heated up to about about 3/4 the way to H and the fan came on and wouldnt bring it back down, so I decided to rev the engine to about 2000 rpm's and to my surprise the engine cooled down when I did this. Does this sound like a water pump issue? I still dont know why it runs fine while I drive in the city or while at low RPM's, but will heat up after being at high RPM's for about 10 to 12 miles.

If there is a coolant flow restriction, then im gonna assume its in the radiator cause the system was fine before I replaced it(no overheating at all and no movement of the temp needle at all.). The order I changed things was:

radiator cause of leak, also changed upper and lower radiator hoses.

Thermostat a week later cause it had started overheating like I said. It wasnt oem cause I purchased the fail safe thermostat to prevent it from failing closed.

Then over this last weekend (which was about 2 weeks after the thermostat) I replaced the fan relay and cooling fan switch that sits in the thermostat housing.

I am not sure if it is oem or not to tell u the truth. It was the only one that the auto parts store carries. It was $80. I scheduled a chem flush and pressure test for thursday to tess the pressure of the system and to see if maybe the added flow of the new radiator may have broke some deposits loose or not.

No nothing was done to the fan or its wiring. It was disconnected while the radiator was changed but nothing else. I changed the ect switch and the relay.

Today before I left work I checked my coolant level ( which was fine) I noticed that I could squeeze the radiator hoses and cause coolant to flow into the overflow tank. So when I got home I decided to see how much pressure would be in the system by pulling the radiator cap and to my suprise I was able to pull the cap without it spewing everywhere! I am going to try the old cap that came with the radiator to see if the same thing can happen. But I do know that is mot suppose to be able to be done. If the original cap can do the same thing, does it sound like the neck to the radiator is bad? Obviously if the neck is bad then the radiator is.

Its interesting, cause I kept the old radiator cap that came with the radiator and when I discovered this I tryed that cap on it again and it didnt do the same thing. All the caps at the auto parts store are exactly the same, only difference is that one is a pressure release and the other is not.

Ok I had my system pressure tested and that was fine but a honda mechanic said that hes seen that before and it was the water pump. So I had the water pump replaced and all the timing components. It seems to have fixed the problem, but there is still a small fluctuation in the temperature gauge. Its only a small amount, maybe an sixteenth of an inch or so, so far. Does this sound normal? Its never moved like that before, that I can remember.

When I replaced the thermostat a while ago I did put a fail safe one in. Maybe that?