Isn't the minimum exhaust temperature the same as the temperature of the heated water? How can it be less?
Also, cold exhaust doesn't exhaust (since it cant rise through a density change). So, if your exhaust is too cold, it will collect in your basement (CO2 should be a bit denser than air, so absent any drafts it'll collect)
The previous owners of my house installed my high efficiency stove improperly using the old brick flue. The fumes eventually ate away at the mortar and a few bricks fell I'm clogging it.
Unless you have a fan blowing smoke into flue. Without fan, my furnace would not work, exhaust is only slightly above water temperature and furnace is designed so that condensate pools in special container, which you have to empty or connect to sewage.