Power consumption is a dominant and still growing cost factor in data centers. In time periods with low load, the energy consumption can be reduced by powering down unused servers. We resort to a model introduced by Lin, Wierman, Andrew and Thereska that considers data centers with identical machines, and generalize it to heterogeneous data centers with $d$ different server types. The operating cost of a server depends on its load and is modeled by an increasing, convex function for each server type. In contrast to earlier work, we consider the discrete setting, where the number of active servers must be integral. Thereby, we seek truly feasible solutions. For homogeneous data centers ($d=1$), both the offline and the online problem were solved optimally by Albers and Quedenfeld (2018). In this paper, we study heterogeneous data centers with general time-dependent operating cost functions. We develop an online algorithm based on a work function approach which achieves a competitive ratio of $2d + 1 + ε$ for any $ε> 0$. For time-independent operating cost functions, the competitive ratio can be reduced to $2d + 1$. There is a lower bound of $2d$ shown by Albers and Quedenfeld (2021), so our algorithm is nearly optimal. For the offline version, we give a graph-based $(1+ε)$-approximation algorithm. Additionally, our offline algorithm is able to handle time-variable data-center sizes.