Although it may seem counter-intuitive, cooling inside a hot case is better than cooling when exposed to open air. Air cooling comes from a combination of air temperature and current. If the air isn't being forced to move, the hot components heat up the air right next to them, creating a boundary layer of hot air which impedes further cooling. (This hot boundary layer eventually floats away due to thermal convection - hot air rises. But nowhere near as fast as a fan can blow it away.)
So cooling is better inside a case with adequate ventilation. The fans create an air current, causing the hot stagnant boundary layer of air around hot components to be drawn away and replaced with fresh cooler air. Even if the fresh cool air inside...