It is called a “hot roof” and it is becoming (is) an approach that is being embraced more and more to create a more energy efficient home. There has to be a way to exchange air however, so you will want to look for an air to air exchange system (warm air going out and warming the cool air coming in). Most builders are exchanging air with an extra bathroom fan some place, on a timer (sometimes in the main hall, upstairs or even in a closet). Or with the existing bathrooms on a timer. The best approach to the timer application is a timer in the basement, tied to the bathrooms. As human behavior proves that people will not use or will shut off or disconnect the fans because they feel like they are wasting heat or energy. Homes need to exchange air. I am a fan of traditional venting approaches. I feel like hot roofs have the potential to affect people"s heath by keeping “stale” air in the home, trapping radon more readily, etc. Not to mention, allowing mold growth more readily if the air becomes too humid. All of this, because people won’t run their fans. The fans should run at least 30 mins per day. I did an inspection a few weeks ago and all of the bathroom fans (3) in the home were running at the same time when I arrived. They were on a timer in the basement.