Why does my Aviator keep overheating, when I changed almost everything?

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I have changed the radiator, water pump, thermostat, fan clutch, and band. And my truck keeps overheating, if its parked and you accelerate it won't overheat. But if you start driving it maybe 3 miles down it will start overheating making the coolant boil over. I bought a new coolant cap, and tried it and drove it and it did it again, put this time the coolant did not boil over, the idle little by little started to move up and got hot again. There was no leaks nowhere and the engine sounded nice and quiet, no smoke what so ever. And you can feel the air from the fans working good. We left it to cool off, later in the day we turned it on, had it on for a while and kept accelerating it, and it the idle would right where it should and it would not over heat at all. Only once you start to drive and step on the gas is when it start to overheat. Its not showing no codes right know, the battery was off for a while.