I think the important thing is it'll run cooler regardless of if it will produce more heat. 
If the external exhaust will output most of the heat into my room instead of letting it stay inside my computer I'm happy. 
Bottom line is, I don't want my computer to burn out.
Thank you all who give their thoughts.
		
		
	 
This is going a bit off topic since  unless your case is really cramped and/or filled with dust, your room temperature is high, your card is defective, etc, none of these cards will die due to high temperature.
But lets look why heat generated may be important.
Even if a cooling system is able to dissipate the heat and drop outside your case, the room will increase temperature due to that heat. That will make harder to cool the rest of your system (unless of course the cooling of your room is really good or your room is cold anyway) - there is a reason why in summer some people have to reduce their OCs even when they are perfectly stable during winter.
Lets take the example of 2 cards with a reputation for being hot - the 4850 and the GTX480.
Both of these cards with their reference coolers could run into high temperatures.
The 4850 was a card that dropped the heat inside the case and the GTX480 was a card that exhausted the heat outside the case.
So which case/room will run cooler?
Obviously the 4850 since it generates much less heat since its power consumption is much smaller.
1 advantage of the open coolers vs exhaust ones is that they aren't as noisy. The fact the high-end cards use exhaust coolers is due to the fact they generate too much heat to just dump it inside your case.
 
In the case of the OP, his X1600 probably has some problem or there is too much dust.
And make sure you have a strong enough PSU. Those pre-built systems tend to have wimp PSU.