There are 2 fans. The mechanical fan immediately in front of the engine free wheels until the clutch (the fined thing on the front of the fan) engages based on the temperature of the air flow from the radiator (Note - the OEM clutch apparently especially the 2005 is prone to failure and in any case triggers the fan a bit late in the temp rise curve so a better option is the Hayden clutch w/without the gasser plastic fan or kaps fixed fan). This fan doesn't "care" about the tstat except to the extent the tstat influences radiator air temp (e.g. a "hotter" tstat will slightly raise radiator air temp but not enough to exceed the clutch trigger point as that air temp is well below the tstat temp unless you are in over heat mode). The electric fan immediately behind the grill is I think primarily controlled by AC operation but what sensors, if any other than the AC high side pressure sensor, trigger that fan to come on (Note it has a high and low speed mode of operation) is somewhat unclear, see
viewtopic.php?f=5&t=64105 . I doubt changing tstat temp would have much if any impact on that fan either.