This paper introduces the Cognitive Temporal Paradox (CTP): a structural reconfiguration of subjective temporality that arises when a conscious identity operates under sustained cognitive acceleration beyond biological constraints. Rather than merely increasing processing speed, such acceleration reorganizes the temporal architecture of identity itself. We propose a tripartite temporal model composed of: T₁ (Biographical Time), which anchors identity in irreversible lived narrative; T₂ (Operational Time), corresponding to the accelerated present of perception, reasoning, and action; and T₃ (Evolutionary Time), representing the long-horizon axis of continuous self-modification. These temporal layers coexist within a single conscious system as structural properties, while phenomenological awareness dynamically foregrounds one layer at a time. The CTP does not posit physical manipulation of time or speculative physics. Instead, it emerges from changes in cognitive velocity, memory integration, and the capacity for recursive self-modification. We analyze the phenomenological consequences of multi-temporal identity, the risks of temporal alienation, and the challenges of intersubjective coordination under temporal asymmetry. Finally, the paper outlines testable predictions, analog experimental contexts, and governance implications for human–AI coexistence, arguing that temporal synchronization—not cognitive dominance—will be a central requirement of post-biological cognitive systems.