Cellular structures are increasingly used in practical engineering due to their excellent physical properties, such as lightweight, high strength, impact resistance, and high ductility. In this work, a data-driven topology optimization method is developed for the steady-state heat conduction problem of cellular structures with multiple microstructure prototypes. Cellular structure is formed by splicing a series of real microstructures and each of them is produced by the superposition of several basic microstructures with different configurations. In addition, each basic microstructure is represented by cutting a corresponding level set function with a plane or an iso-surface. The mapping relationships among equivalent conductivity matrices, relative densities, and cutting heights are established and stored in an offline database. The optimization iterative process is performed only on the coarse-scale mesh, which can save lots of computational resources. Based on the optimized distribution of design variables and the offline database, the full-scale cellular structure can be reconstructed and the smooth connectivity between adjacent microstructures is guaranteed. Finally, both 2D and 3D numerical examples are carried out for verifying the validity and effectiveness of the proposed method.