I have a 2003 ford Explorer and sitting idle is does not overheat but when I drive a few miles it overheats.

Or the fan clutch cold be bad.

I have a 2003 explorer. When I changed the water pump and changed the fluid it took a good long time for the thermostat to open at idle. A lot more time than one would expect it at idle.

By simple design, almost all cars do not require an engine cooling fan of any kind over 30 mph unless pulling a heavy load. Stock Cars don't even have fans. Thermostats these days are designed to fail open (I guess thermostat manufacturers got tired of having to buy engines) - making the engine run cool. Do not expect any engine to get warm enough to open the Thermostat at Idle. For Diagnostics, Ford recommends 2500 - 3000 RPM for 3 minutes just to get it up to operating temp and 5+ minutes to open the thermostat (that's without driving it). Having said all of that, A blown Head Gasket, worn down Water Pump impeller, incorrectly installed serpentine belt (spinning the water pump backward) or a plugged up radiator. If it overheats quickly - I'd do a compression test. Don't forget to check the Pressure Cap (radiator cap).

Was the sending unit (on the thermostat housing) changed when the stat was changed? Check to make sure the wires were not damaged. Is the vehicle really overheading, or are you going by the light/guage on the dash?

I believe if the engine is over heating it would throw a code and idiot light on the dash, are you getting one?