The unexpected diversity of exoplanets includes a growing number of super-Earth planets, i.e., exoplanets with masses smaller than 10 Earth masses. Unlike the larger exoplanets previously found, these smaller planets are more likely to have similar chemical and mineralogical composition to the Earth. We present a thermal evolution model for super-Earth planets to identify the sources and sinks of atmospheric carbon dioxide. The photosynthesis-sustaining habitable zone (pHZ) is determined by the limits of biological productivity on the planetary surface. We apply our model to calculate the habitability of the two super-Earths in the Gliese 581 system. The super-Earth Gl 581c is clearly outside the pHZ, while Gl 581d is at the outer edge of the pHZ. Therefore, it could at least harbor some primitive forms of life.