I suggest a neutral density filter in that case, but I suspect the Coronado engineers probably have a pretty good idea what they are doing, so I don't know if you'll achieve much. Give it a whirl though, there nothing to lose!
The PST is supposed to be designed to be thermally stable when viewing the sun. My observations are that if you look though it as soon as it points at the sun, the image is not as clear as after a few minutes when the scope reaches thermal equilibrium. That suggests to me the designer's knew what they were doing...
Al.