Computational homogenization methods reveal the physical behavior of heterogeneous materials, often complex due to intricate manufacturing. Micromechanical techniques use microstructural data to predict effective behavior. However, processing digital material data, represented as voxels, involves handling numerous image points. While modern FFT-based solvers are powerful, performance improvements remain beneficial. The composite voxel technique, in its original form, enhances accuracy by applying a surrogate material law to voxels containing more than one material phase. This work contributes to the understanding and application of composite voxels for thermal conductivity problems by integrating them into a level-set-based framework. Using FFT-based solvers, we demonstrate their potential to enhance computational performance through numerical examples.