We know that RECIRC FAN could reduce the packs' working load
Recirculation fans have no effect on pack workload. It's myth and poorly written in the FCOM.
With recirculation fans OFF, the airflow in the cabin is below what is required for certification, but it doesn't change the workload on the pack.
Had Boeing build the aircraft without recirculation fans, they would have had to make the pack deliver more airflow in order to make certification requirements.
Hence, the recirculation fans saves fuel (as written in the FCOM),
compared to if the aircraft was built without recirculation fans.
In any case, recirculation fans off, doesn't increase pack load and subsequent fuel consumption (you won't find anything about increased fuel consumption in the MEL either). But if the aircraft is full, your cabin crew will most likely complain that they can't breathe in the cabin and ask you to turn the temperature down, even by normal temps (as they can't find any other reasonable explanation for the sticky air).
P.s.
My QRH have no mention of the recirculation fans in the pack trip off NNC. What 737 do you fly?