2006 Chevrolet Impala cooling fan

firefighterf: not knowing exactly what engine of the three you could have in your car: 3.5, 3.9 and 5.3, I could only study up on technical service bulletins and recall some of the cars i have had in my shop with cooling system problems.
GM used "DEXCOOL" antifreeze which had a problem that caused corrosion and reeked havoc with the cooling systems on many of the vehicles they used it in. There was a service bulletin out on this matter to address a procedure in flushing the systems. There were quite a few cars which needed radiators, water pumps and heater cores replaced from the corrosive damage done by the DEXCOOL.
Check your car and make sure that you have not got a situation pending where the cooling system is fixing to leave you stranded or burn your engine up.
The V-8's didn't really have any problems with cooling systems which were mentioned in service bulletins other than that one.
The 3.9 liter had a problem with head gaskets leaking coolant. The leaks would appear to be coming from the top end(s) of the cylinder head(s), leaving small deposits of coolant on the ground after sitting. A new gasket design came out to resolve the problem.
The 3.5 had a problem with head gaskets as well and additionally a problem with leaking "crossover " pipe gaskets.
Add this to the issue with the corrosion problem of the DEXCOOL and you have a serious situation. Keep in mind, that often people open the radiators or cooling system recovery tanks when they might still have some pressure in them. Coolant spills or sprays around the immediate area, including near the "FAN GROUND LEADS". If you end up with poor grounds, you will develop problems with any electrical components which rely on those ground circuits. NOW! Here is some more food for thought that few techs have ever told customers. A coolant temperature sensor is designed to be immersed in coolant or water. The heat transferred from the water or coolant to the temp sensor, causes the sensor to change resistance values which in turn, will make relays go on an off, give input to the ecm for it to use as part of the data needed to control pulse width of the injectors, and guages indicate the temperature. One phenomenon that occurs when the coolant level drops to where it no longer has the coolant sensor immersed, is that the sensor will no longer read correctly. You temperature guage in you dash may indicate the engine is at normal operating temperature and the engine may be in thermal nuclear melt down!
Steam in the cooling system will not have the same effect make the sensor register hot!
I hope that I may have given you some direction in which to look.
My not knowing the particulars, I tried to cover as many bases as I could other than dealing with relays, fuses and wiring. I would need the specifics on YOUR car to be able to better assist you.