This definitive work closes a long-standing gap in antiferromagnetic switching certification by transforming thermally assisted switching from a theoretical allowance into a functionally certifiable mechanism under fixed, replayable rules. Just days earlier, Magnet Switching Under a Plateau Corridor: G–Σ–P–L Grammar for Two-Mechanism Antiferromagnets established a plateau-corridor grammar that successfully certified roughly 80–90% of practical switching behavior, covering the dominant non-thermal regime with durable falsifiers, parity hygiene, and tokens-only replay. In that earlier framework, thermally assisted switching was acknowledged as physically plausible but could not be certified without reopening the door to threshold travel, post-hoc filtering, or narrative repair. The present work resolves that limitation. By importing a signed thermodynamic ledger directly into the corridor grammar, thermal involvement is no longer inferred or excused—it is forced to appear as explicit ledger structure. Ambiguity is recorded rather than averaged away, yield loss is charged rather than hidden, and approach to instability is monitored by a monotone collapse witness rather than rescued by retuning acceptance. As a result, the thermal boundary becomes a certified branch line rather than a movable threshold, and thermo-assisted switching becomes operationally distinguishable from non-thermal switching under the same fixed contract. This advance converts a previously blocking regime into a usable, auditable engineering option. The combined framework preserves the plateau corridor as the default engine for the majority of switching cases, while extending certification cleanly into the remaining hard boundary where thermal assistance and non-thermal mechanisms coexist. The output is not a single best curve, but a stable branch map that identifies certified non-thermal regions, certified thermo-assisted regions, and refused boundary haze—each paid for explicitly in accounting. In doing so, the work prevents false unification, enables honest device comparison, and completes the switching grammar at the exact point where informal analysis most often fails.