My car was recently acting up, we did a diagnostic test on it and it came up showing that the Cooling Temp Sensor was bad and needed replacing. I bought the sensor, got ready to do a quick little unplug, plug in new sensor job. I looked under the hood for about 30 Minutes and I did not see one damned thing. I can't find the sensor anywhere. Does anyone know where the Cooling Temp sensor might be?

It's a Buick 3.3L

Life, (Name ???)
Dont know for certain on your vehicle, but most "real" parts stores have a sensor locator book that tells the location of most sensors. The store where you bought your sensor should be able to tell you where it is located.
Hope this helps,