TOPIC: Roof: How hot is hot? Question concerning a ranch with no attic

And lets not overlook the problem of two layers of shingles (tiles?)  IRC states only one layer is OK.  4 year old roof should have been a complete tear off. 

Thank you gentlemen for the extra questions:
The house is a single story low-slope gable (not a hip) with a vaulted ceiling in the livingroom on one end and a vaulted bedroom on the other.  There is 1 one-square foot gable vent on the wall, under one peak, on one side of the house.  Still not sure if the perforated vinyl soffit is covering the old soffits (or even if there were any to begin with because I can't find a way to get a draft with my smoke stick).  The three bedrooms, kitchen, two baths in the middle section of the house have 8' flat ceilings.  There are no accesses anywhere.  My friend and I have looked in every closet, etc.
This house is used mostly in the fall and winter during ski season.  I stayed there all last week and inspected it a few times while I worked out a new report template.  Needless to say, the heat that built up on the roof, radiated down by night time and kept the house temp at almost 78 degrees. 

Thanks again for the help.
BTW Dennis, love the profile image...

Ok, that sound more familiar.  I think you are right to be concerned, especially about the section of attic space with no access point. If you had a ladder to reach it, taking a look into the gable vent might provide some limited perspective. This may provide greater info depending on the size of the vent or if you could get a borescope into the opening.  Accessing the eaves seems a bit impossible from what you described.  You might try your smoke test at the gable vent to see if it is drawing air in or out, but I'm not sure what you may conclude from that. 

The ventilation at the vaulted ceilings may or may not be an issue. If they are rafters with insulation sandwiched between interior and exterior finish, then the type of insulation would determine if there is a concern.(i.e. a “hot” roof or ventilated).  If the roof framing is a truss system with a different pitch to the interior ceiling, then the whole attic may be addressed  the same as the space over the bedrooms

The combination of retrofitted ridge and soffit ventilation, a low slope roof and dark shingles all point to a system which will not be very effective at passively removing heat. Personally, I've reached the point where mechanical ventilation is my recommendation of choice.  Passive ventilation is too dependent on environmental conditions and people not screwing it up.