do you mean a metal line with a hex fitting that is connected to the radiator side tank above the large hose at the bottom battery side of radiator? if yes, that is for cooling the transmission fluid, but no coolant runs through those two steel lines, only transmission fluid is circulated through the radiator by the top and bottom steel lines.

if not that, do you mean the coolant expansion-recovery tank located under the battery that has a smaller hose connected to the radiator filler neck?

otherwise, as far as I know, there are only two radiator hoses from engine to radiator, top and bottom. unless you mean the Heater hoses on top of the engine which form a "Y" split.

a possibility is that someone installed a coolant Heater in that hose. A picture would be great.