Why does excess combustion air increase fuel consumption?

On page 83 of his book, Wardale quotes a 19th century writer, saying:  “We were trying to keep out of trouble by preventing smoke, but soon found that the prevention of smoke and the saving of fuel did not agree. If you prevented smoke, you burned more fuel.”

Chris Newman asked why this should be so when smoke emission was indicative of carbon carry-over and therefore wasting of fuel.

Wardale answered as follows:

“Because smoke prevention was achieved by high excess air, hence high smokebox gas loss (and is to this day on the new SLM rank tanks, which operate at far too high an excess air coefficient).  This loss of heat can be far greater than that carried away in soot (smoke).”

In a 2001 letter to Newman, Wardale qualified this statement saying:

“The excess air in the SLM locos is too high for best efficiency, and is thus to dilute the pollutants. It is not a question of a difference of opinion between myself and Roger Waller. We both know that excess air should be kept to a minimum for best boiler efficiency but he sees the diluting of pollutants as a more worthy goal.  I would go for both.”