This paper introduces Thermodynamic Memory Salience (TMS), a physically grounded retention filter for persistent AI agents. Rather than retaining all experience or discarding memories by age, TMS scores each memory at formation time using the thermodynamic state of the physical substrate on which the agent runs. The salience equation S(m) = α·ΔH + β·ΔL + γ·D combines hardware entropy delta, load delta, and informational deficit to determine which memories persist and which decay. Version 2 updates Section 4.2 to document the Graceful Degradation Protocol: when hardware temperature sensors are unavailable in containerized or serverless environments, the system executes a standardized instruction-cycle timing measurement and maps execution jitter to a thermal proxy. The substrate remains physically measured across all deployment environments. Empirical validation on Apple Silicon hardware demonstrates discriminative retention: high-novelty inputs are correctly promoted to long-term memory while repeated routine cycles decay, with physical substrate state determining which borderline memories cross the retention threshold. Third paper in the PermaMind research arc. Paper 1 established the Law of the Informational Deficit. Paper 2 introduced the Osiris-Set-Isis autonomous stagnation prevention cycle. TMS completes the arc by answering what a persistent, self-renewing agent should remember.