'05 Taurus cranks but hard start. Seems to occur when it is below freezing. Original battery in car. Battery was tested and told it was bad. New battery in and car cranks nice and started right up , although it is 32 deg. right now.Is it possible for the battery to turn the engine over under normal conditions but when below freezing doesn't have enough power to start the car?

 

Yes.
The battery works on a chemical process. When it is cold the process slows down. At some point it it won't deliver enough juice to start the engine.

 

The "gist" of the situation with a battery "working hard", as while cranking over an engine, is that it's output voltage drops while it is doing the hard work. How much it drops is related to the battery's internal condition, as well as numerous other factors associated with getting the "juice" to the starter motor.

Ignoring those other factors, as the battery's output voltage drops, so does the effectiveness of the spark delivered to the spark plugs, making "firing" of the engine more difficult. The low temperature factor causes gasoline to be more resistant to evaporating, or vaporizing, which is necessary to allow firing.

Fun, ain't it? imp

 

Yes, the battery is very likely to have just enough 'chemical reaction' left to spin the starter, but not have just enough to power the other systems required to start the car, like the fuel pump and fuel injection. Escorts were really good for this, also.
One thing to keep in mind if the power supply system is in good shape is that this powertrain (3.0L vulcan or DOHC) had a tendency at about freezing to flood the engine. I've done this for years, and it only happend on this powertrain at about this temp. No one at ford has ever explained why this is, especially as the older body style hardly ever had this problem.
Hope it helps.

 

Indeed that's fun! And there is another layer to it: as it gets cold the electrical resistance in the wires is dropping. If it were not for that it would require some monstrous batteries to get anything going.

 

Yes, you are correct, electrical resistance drops as temperature drops. Unfortunately, in the range of temperatures we experience in starting engines, that resistance change would only become significant in affecting the operation if the conductors (cables, in the case of starting) were too small in cross-section.

You could measure the "voltage drop" across the ends of the cable "feeding" the starter motor, while cranking, at operating temperatures, say 100 degrees, and again when cold. Doubtful if all other things were the same, (battery state of charge, mechanical condition of starter motor, electrical contacts in solenoid(s)) that the voltage drop would vary by more than a few %. Might make an interesting experiment, or it could be calculated knowing the conditions present.
imp

edit: At one time years ago, there was a "rash" of hard-start engines typically encountered in only one make and model. Someone else can reveal which, not me!