Firstly, I am going to assume you are meaning "STEAM", and not "SMOKE". The two would indicate VERY DIFFERENT issues... if you have SMOKE, there may be a much more serious issue than described below....
Sometimes the coolant system needs to "equalize" after a drain/fill... It may just need to "cycle" a couple times up to full temp, even if the pressurized system is "spilling" over into the overflow. Sometimes, the overflow bottle can "overflow" until the "HIGH/LOW" point balances out. This process may also require "BURPING" the system, or "PURGING" the air within the water jacket/loop within the cooling loop. This is accomplished by starting and warming up the engine (from a cold state) with the radiator cap OFF. Initially, the coolant will just "sit there" unaffected by the running engine.... once the coolant/engine begin to come up to temp., the thermostat will open, and coolant will begin to circulate... (you'll see it "agitating"...let it circulate for a few moments...) After a few more moments, the coolant should "rise" and begin to "burble out" of the radiator. Now it's fully circulating and expanding from the heat. PUT THE RADIATOR CAP BACK ON! You've just "burped" your system. What is happening here is, there may be "AIR POCKETS" within the cooling system loop. Especially if it has been FULLY DRAINED and filled. Sometimes, this "AIR POCKET" can get to the "water pump" impeller area, and cause "CAVITATION", or "free-air pumping", wherein no HYDRAULIC action is taking place. In this state, the system will begin to overheat, until the "cavitating" air pocket in the system is "bled" or "burped" from the system...
I also think the thermostat COULD be "sticking" closed. This sometimes happens just after a change if it is OLD... or may just "start happening" without any change... You should observe your initial "start-up/warm-up" period... where the temp. gage is coming up to the point where it usually "levels off", or holds steady once everything is up to temp.... watch closely, and as you begin to drive, does the temp. gage go ABOVE the usual point for a short while... then come back down again after a few minutes of driving at temp? (Sometimes, if the thermostat is sticking "badly", the temp. will shoot up to RED or FULL gage temp. for a little bit, then all of a sudden, the thermostat "pops" open, and drops back down.... if the thermostat is NOT popping open at all, then it must be replaced IMMEDIATELY, as you will overheat and damage the motor.
(What is going on with the thermostat is this: When you first start a car, the engine is cold. In order to generate warmth "quickly" to bring the engine temp. up to PROPER operating temp. the thermostat is "mostly" or "all the way" closed. This means little or no coolant is circulating... until temp. is within thermostat range, then it pops open, and begins to circulate.)
The OTHER thing that comes to mind is your radiator cap may be worn or not "seated" well after the change. Some coolant may be getting out around the cap and "evaporating off" as steam.
Phew! Did I just type all that?
Actually, be careful.... I don't really know ANYTHING about cars.... but I DID sleep at a HOLIDAY INN EXPRESS last night!!!
-crisp
