First if you fire up the engine, radiator cap off and the coolant starts "racing" immediately or shortly thereafter like boiling water it's a sure sign a head gasket is blown especially if there is a burnt smell in the radiator neck to include oil mixed with the coolant right there and that being the case I would do BOTH gaskets assuiming the heads don't need to done.
I'm curious as to the where the white smoke was coming from in the engine bay....leaking somewhere or what...?
Most engines will emit some white "moisture" smoke out the tailpipe at cold start, hot air over cold pipes then dissapates...NBD.
If you fired it up cold and everything was fine with no over heating issues you may have dodged a bullit but I would change the oil and filter immediately just to be safe and then I would put a pressure gauge on the radiator neck and check for any leaks, definately make sure the thermostat is in correctly with the designated OEM degree, mine is 195* thermostat for a stock 302/5.0L EFI.
The way to tell if the thermostat is working properly would be where the upper radiator hose should be hot and you run and shut off the engine otherwise it's in backwards.
Make sure all your fan belts have the correct tension so the fan blade is working optimum.....
However if this overheating persists then you have a decsion to make $$$$$
Good Luck ~ :thumbup