I think usually the warranty covers a remanufactured part unless they are out so you would have a brand new part.
Without a new car warranty, most parts are covered for only 12 months or 12,500 miles except for a very exception: Your Drive Unit is covered for 4 years or 50,000 miles whichever first.
The sticky part is if your replacement is covered under the new car warranty of infinity miles or 8 years whichever first, then if it dies the next day when that new car warranty expires then can you claim the part warranty too or not.