This piece by Engadget provides an excellent and clear (thankyouverymuch) description of how contemporary digital projectors work. Whether a technology has moving parts or not, heat is always an issue. For digital projectors that literally millions of mirrors that are in constant motion. The cooling approach is twofold: the microchips covered with mirrors have "spiky-looking heat sink" as well as liquid coolant piped throughout. While the piece covers heat management, it also provides general and user-friendly projector details.
The "must" of this post is the video. Using CGI (naturally) Science Channel has modeled the inside of these complex machines.