The excess fuel is not cooling anything. It is merely lowering combustion temperature, and delaying peak pressure, much like retarded timing.
Lycoming data lists what they consider to be the
minimum fuel flow for rated power, which includes a detonation margin. Power output is fairly flat in the region richer than optimum, so it is possible to run richer without huge power loss. Setting up the fuel control to be richer than the minimum required for rated power adds additional detonation margin. Recall that best power mixture is about 100F ROP, and we like to see the fuel control set up for 200 ROP at full rich, maybe 250. Some like it even richer, but that's just an expensive way to make less power.
BSFC (pounds of fuel per HP per hour) is a fine guide to fuel flow, IF you know power output with some accuracy. For example, my IO-390 manual says minimum fuel flow is 105 lbs at 210 HP, for a BSFC of 0.50. A 260 HP engine at 0.50 is 130 lbs per hour, or 130/6 = 21.66 GPH. The consensus 25.5 would be a BSFC of 0.588.
Here's a useful chart from the FAA dyno, an IO-540-K. Lots of interesting things to observe, but in the context of this discussion, note the BSFC and fuel flow at max power mixture; 245 HP at 112 lbs per hour, for a BSFC of 0.46, or 18.6 GPH.