Engine 99 Mustang 5.4 Dohc Swap

hello everyone. I am new to this forum and its my first time posting a thread. I am in progress of swapping 5.4 4V (out of navigator) into my 99 mustang gt with 302 boss intake manifold and mmr adapter plates. I am using 99-01 cobra thermostat housing and I have connected all the coolant hoses to the engine and radiator. But I still have an extra tube that in coming out of the engine under the intake manifold to the left of the alternator. And it has 2 outlets. Does this tube go the heater core? If it does, where I am suppose to connect the other heater core to?
Thnx Guys

I could not get a clear photo using my iphone because the camera is broken. But I found this picture from google and it show the tube I am talking about.

wmburns said:

If looking for an educated guess, the large line is the heater return from the back of the water pump. The smaller line is for the degas/overflow bottle.

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Thanks for replying.
-So do I have the degas/overflow bottle in my 99 stang? Is it the coolant tank? I do not have an extra input in the coolant tank. Do I need to connect it by a T shap connector?
- I am not planing to eliminate the heater. I think it help to cool down the engine due to more coolant fluid in the system(Correct me if I am wrong). So where does the heater feed connect to?