A condensation management system, a furnace having the condensation management system and a cold end header box employable in the condensation management system are disclosed herein. In one embodiment, the condensation management system includes: (1) a first drain hose positioned to drain flue condensation from a flue pipe of the furnace, (2) a second drain hose positioned to drain the flue condensation from the flue pipe and (3) a condensation collector box configured to collect both the flue condensation and combustion condensation from a heat exchanger of the furnace, the condensation collector box including at least one drain for draining both the flue condensation and the combustion condensation therefrom.