Power-to-Ammonia-to-Power (P2A2P) systems in hot-arid MENA climates reject waste heat through Recuperated Organic Rankine Cycles (RORCs) whose condensation temperature tracks ambient conditions across annual swings exceeding 35 K. Standard exergoenvironmental assessments evaluate priorities at a single dead-state temperature, an assumption this study terms the Static $T_0$ Fallacy. A four-way advanced exergy decomposition is combined with an off-design model (Stodola’s ellipse, constant-$UA$ scaling) to sweep the dead-state temperature from ${5 }^{\circ }$C to ${40 }^{\circ }$C. At $T_0={20 }^{\circ }$C, 95.8% of total exergy destruction is endogenous, confirming weak inter-component coupling. The condenser carries the largest avoidable environmental impact rate (4.02 mPts/h, 74% of the system total). At $T_0={37.4 }^{\circ }$C, the recuperator undergoes a priority inversion from destruction-dominated ($f_b=14.7\%$) to fully capital-dominated ($f_b=100\%$). Ammonia’s wet-fluid thermodynamic coupling eliminates the recuperator’s duty as the condensation temperature approaches the cold-side outlet constraint. The recuperator’s avoidable environmental impact rate drops by 100% relative to the standard assessment, while the condenser’s rises by 49%. This inversion mechanism is fluid-specific: the ammonia recuperator’s endogenous fraction reaches 99.5% at $T_0={20 }^{\circ }$C. The toluene recuperator, swept at its own independently optimised operating point, has an endogenous fraction between 59.08% and 82.31% over the same range. For P2A2P installations where the annual ambient swing exceeds 15 K, exergoenvironmental analysis should be performed at both design-season and summer-peak dead-state temperatures, with the summer-peak result governing capital allocation.