Oil cooler?

I'm shopping for parts to do a timing belt change. I'm going to do the water pump while I'm there. I keep seeing kits that say "with oil cooler" and "without oil cooler". To wit: "this water pump has a water pipe located on the thermostat housing and is used with models equipped with a oil cooler".

Is my truck equipped with an oil cooler?

 

I believe it's any model with the factory tow package. It includes tranny(on autos) and oil cooler.

 

I just went out and looked at it. There is a hose coming out of the thermostat housing near the block. It comes out towards the driver's side, then turns back towards the firewall and runs over the oil filter to somewhere in the dark.

Does that indicate that I've got an oil cooler?

If so, why does *that* impact which water pump I buy?

Thanks for the help,

Matt

 

I think I see it now, looking at a picture of a water pump. The thermostat housing is part of the water pump and the nipple for the hose I saw attaches to it.

Right? Right?