It might make more sense to get a new video card than to spend $30 to $40 USD on a replacement cooler for a card that's been out for over four years. There are more recent cards in the same price range that draw significantly less power than an X1600 Pro while offering similar to slightly better performance. At least here in the US, you can currently find
fanless HD 5450s at Newegg for around $40 shipped, with some for $25 to $30 after rebate.
Granted, you could likely reuse an S1 or other premium cooler on a future card, though an S1 might be overkill for a card primarily used for desktop purposes. You could also likely find a suitable lower-end cooler or replacement fan that would work with an X1600 Pro though. You might also check whether the existing heat sink and fan just need to be cleaned to make them reasonably quiet again.