The unexpected diversity of exoplanets includes a growing number of super-Earth planets, i.e., exoplanets with masses of up to several Earth masses and a similar chemical and mineralogical composition as Earth. We present a thermal evolution model for a 10 Earth-mass planet orbiting a star like the Sun. Our model is based on the integrated system approach, which describes the photosynthetic biomass production and takes into account a variety of climatological, biogeochemical, and geodynamical processes. This allows us to identify a so-called photosynthesis-sustaining habitable zone (pHZ), as determined by the limits of biological productivity on the planetary surface. Our model considers solar evolution during the main-sequence stage and along the Red Giant Branch as described by the most recent solar model. We obtain a large set of solutions consistent with the principal possibility of life. The highest likelihood of habitability is found for "water worlds." Only mass-rich water worlds are able to realize pHZ-type habitability beyond the stellar main sequence on the Red Giant Branch.