Hi colsonr,
The radiator with cooler attachment are for automatic transmission fluid cooling and is not related to what your are experiencing.
A little white smoke and some dripping out of the exhaust is normal if the humidity of the atmosphere is high, especially early morning or rainy weather.
However if the engine is running rough and the smoke, (actually is steam if it is white), then it could be a faulty head gasket.
After replacement of the radiator, was the system bled of air trapped?
Did you check the radiator coolant level?
Before replacement of radiator, did the engine ever overheated? Up to a few months back?
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Tuesday, July 13th, 2010 AT 9:04 AM