I have aford tempo and it is purging in idle and there is black smoke coming out of the exhaust

Black smoke means it's running rich, which could be leaky injector(s), bad coolant temps sensor, poor spark, bad plugs, bad fuel pressure regulator, and many others.

White smoke is water in the cylinders/exhaust. (bad head gasket) White with a bluish color is oil. Black smoke is to much fuel. Which do you have.

worn out piston rings require replacement..

have you just came out from the car wash... if on normal driving or idle, water is a byproduct of engine combustion, the black smoke may indicate loose or broken piston rings..

first of all u need to determine what color of smoke it is and is it coming out of the exhaust pipe. black smoke means excessive gas burning ...blue smoke means burning oil ...white smoke if seen in warm weather conditions means coolant leak into cylinder heads... but as running rich and high low idle might have a vacuum leak or carburetor need new base gasket or rebuilt ... good luck

You've done a lot of work. How does your EGR valve look Its the 'space ship' gizmo under the air cleaner. Remove and decoke is a quick job and it may just cure the lot

remove the covers and with the key in the acc position look for a pin to push in ,push it in and then pull on key and the lock will come out

check
ingectors maybe one not working
spark plug
air flow mass
feul sensor

If you are sure it is white smoke and the car overheats or looses water,The head gasket is bad.
Or It's valve seals or rings smokes (but the smoke would have a blueish tint)