Continuing 'Roof turbines, are they a good idea"...

I have an old and small two story house that gets very hot upstairs. I just checked the
roof vent situation and discovered there were no soffits, and the two vents, one on
either end of the house just under the ridge, are 7 inches high and 12 inches wide. I
measured the air temp difference and outside the vent it was 72 degrees and 4 inches
inside the vent 86 degrees. This was on the cool end of the house, probably a larger
difference on the other end. I also saw there was no insulation above the ceiling. The
max distance from the ceiling to the ridge is about 2 feet. The ceiling area square
footage is about 500 sq ft.

I had no sense of any convection or air movement out of these two vents, could they be
just too small to do anything?

Given the situation, and the fact that the area where the soffits would be is covered
with asbestos siding so not something I can easily cut holes in, what should I do?
Enlarge the small roof vents, add a roof turbine, something else?


John