Temporal graph classification plays a critical role in applications such as cybersecurity, brain connectivity analysis, social dynamics, and traffic monitoring. Despite its significance, this problem remains underexplored compared to temporal link prediction or node forecasting. Existing methods often rely on snapshot-based or recurrent architectures that either lose fine-grained temporal information or struggle with long-range dependencies. Moreover, local message-passing approaches suffer from oversmoothing and oversquashing, limiting their ability to capture complex temporal structures. We introduce T3former, a novel Topological Temporal Transformer that leverages sliding-window topological and spectral descriptors as first-class tokens, integrated via a specialized Descriptor-Attention mechanism. This design preserves temporal fidelity, enhances robustness, and enables principled cross-modal fusion without rigid discretization. T3former achieves state-of-the-art performance across multiple benchmarks, including dynamic social networks, brain functional connectivity datasets, and traffic networks. It also offers theoretical guarantees of stability under temporal and structural perturbations. Our results highlight the power of combining topological and spectral insights for advancing the frontier of temporal graph learning.