JC stated: "...and the heated walls are at a higher temperature. So, it must get hotter." What makes you think that the walls of the vertical section (i.e., the 'chimney') are at a higher temperature than the walls of the horizontal section that has water at a much lower temperature entering, and the liquid water has a MUCH larger specific heat than the vapor in the chimney? The majority of the heat from the exterior heater around the reactor section willl be flowing back towards the cooler section where the cold water is entering... that is where the largest delta-T is.
-Mark