Have a Dodge RAM truck running hot! It sits and idlkes and has no problems! Drive it and it boils! Flushed radiator, changed new clutch fan, new belts, new thermostat, new water pump! Still runs hot!

Also the heat is still hit even without the thermostat!

Did you just flush the radiator or did you do a cooling system flush ?

Just flushed it with a water hose! The radiator is clean as new! So is the block! It shows running hot but the oil stick never gets hot and it only steams out the over flow!

It may look new but you can not see what's happening on the inside of radiator and block should do a cooling system flush to be sure.

But does that explain why it only runs hot when you drive it? Sitting in idle for four hours in the driveway it will not run hot!

Still would flush cooling system but going by what you are saying try cleaning the radiator or if A.C condenser sits in front of radiator clean with a garden hose and nozzle or better yet a pressure washer using the fan tip nozzle and do not hold to close can bend the fins if partially clogged with dirt and bugs can cause low air flow at driving speeds. Also would not rule out propeller fins on water pump is broken and not circulating anti freeze through system not over heating at idle but not circulating fast enough at driving speeds.

Perform a Block-check. You may have a blown Head Gasket

This may not be real pertinent but years ago my 1973 Chev Monte Carlo, which I used in my business of delivering work I had done, would overheat going on the hill between Los Angeles and the San Fernando Valley. I had a great mechanic at the time, believed in old fashioned fixing. Anyway, nothing wrong with the car so he suggested replacing the radiator with a larger one.. I did and he was right. Never had an overheating problem and had no problem driving through the desert for years from San Fernando Valley to Las Vegas. I still have the car and it still performs as it should. Just a thought......I am not an expert but I did have the above experience,