As 3D content creation continues to grow, transferring semantic textures between 3D meshes remains a significant challenge in computer graphics. While recent methods leverage text-to-image diffusion models for texturing, they often struggle to preserve the appearance of the source texture during texture transfer. We present TriTex, a novel approach that learns a volumetric texture field from a single textured mesh by mapping semantic features to surface colors. Using an efficient triplane-based architecture, our method enables semantic-aware texture transfer to a novel target mesh. Despite training on just one example, it generalizes effectively to diverse shapes within the same category. Extensive evaluation on our newly created benchmark dataset shows that TriTex achieves superior texture transfer quality and fast inference times compared to existing methods. Our approach advances single-example texture transfer, providing a practical solution for maintaining visual coherence across related 3D models in applications like game development and simulation.