Having recently installed such a gable-vent fan (15" diam, ~1500cfm)
for an attic of over 1000 sq.ft., with eave vents of a bit over 2
sq.ft. at each end ...

Thermostat that came cabled to fan has ~15 deg. F differential, makes
on rise at setting from ~60 to ~130 deg F IIRC. Mfg suggestion: set to
105 deg F. (Thus switches off at 90 deg. F.)

Set to 105 deg. F, I wouldn't wait around for it to switch on in
winter.

Meanwhile, I've a temp/humidity logger sitting in the attic, to see
what's happening over the course of a week. Fan motor is rated to draw
4 a., but it sure doesn't output 1/2 hp. Real_soon_now, a kill-a-watt
will have to go into the circuit to collect some data.

Biggest challenge in installation was in making a transition from 1/2"
ply to connect fan to existing eave vent. Couple hours' cobbling about
got it done. Otherwise, whole upper section of attic end-wall would
have required r&r. Maybe some additional soffit vents later.

When fan runs, a little smoke lets me see gentle airflow across attic.
Not "dead air." I'd ensure that air inlet was as far away as possible
from exhaust fan, for single inlet.

Opening door into attic enables using fan as effective whole-house
vent- maybe a timer-switch for that soon too. For those sunny fall
days.

HTH,
J