prevailing paradigm in modern chemical oceanography posits that a warmer climate suppresses marine primary productivity via enhanced thermal stratification. However, whether this transient mechanism holds true for long-term equilibrium greenhouse states remains a critical uncertainty. Here, we utilize the cGENIE earth system model to investigate the behavior of the biological carbon pump during the Late Cretaceous ($80\text{~Ma}$) and the Guadalupian ($262\text{~Ma}$) greenhouse periods under variable dust-derived iron fluxes and $\text{PO}_4$ inventories.

Our simulations reveal an inherent high-productivity tendency in warm oceans, where global particulate organic carbon ($\text{POC}$) export capacity is fundamentally elevated despite geographically disrupted physical upwelling. To resolve this paradox, we propose a new "Hierarchical Control Framework" governing the greenhouse biological pump. Temperature operates as the primary control by accelerating surface nutrient uptake kinetics and subsurface heterotrophic remineralization rates. This dual thermodynamic forcing shortens the remineralization length scale, trapping nutrients within the upper $500\text{~m}$ and driving a pronounced shoaling of the global nutricline. Consequently, a highly efficient, high-turnover "shallow hyper-cycling loop" is established, allowing baseline physical upwelling to carry an enriched nutrient payload.

Conversely, nutrient availability—modulated by the global $\text{PO}_4$ inventory and dust-derived iron supply—exerts a secondary control. Rather than capping the system's baseline thermodynamic capacity, iron limitation acts as a critical "brake pad." In sensitivity experiments where iron limitation is removed, the biological pump immediately surges to its temperature-driven ceiling, triggering catastrophic, runaway global marine anoxia.

Our findings demonstrate that deep-time Oceanic Anoxic Events (OAEs) and biotic crises (e.g., the Capitanian extinction) do not strictly require massive external nutrient pulses via accelerated weathering. Instead, they can be internally ignited by shifting iron dynamics within a highly volatile, temperature-primed ocean. This long-term biochemical reorganization highlights a non-linear planetary feedback that challenges traditional linear extrapolations of transient anthropogenic warming impacts on future marine ecosystems.