The roof is pyramid shaped (about 30 x 30 ft, tan-colored shingles) with
soffits on all sides and several passive vents mounted near the peak, as
well as a powered fan with a 15" diam. opening. A few weeks ago I took
the large steel dome-shaped top off this fan unit and added more screen
and raised this dome by about 10 inches. This allowed the fan to move
the air out of the attic more freely without developing any
back-pressure. The existing height allowed for about 3 inches worth of
clearance for the air to be expelled. This modification alone was
enough to drop the attic air temp by about 5 to 10 degrees.

A few days ago (wed or thurs) I set up one of my sprinklers on the roof
and watched the attic temperature drop after a few minutes of watering.
I collected the water in a couple of 55 gallon plastic barrels and let
the water cool over two days to water various plants. Naturally, the
water was quite warm as it came out of the downspout and into the
barrels. I have a temperature sensor mounted about 1" under the plywood
roof deck in the attic and it went from about 120F to about 100F during
the watering.