The Fermi Paradox questions the lack of evidence for advanced extraterrestrial civilizations despite the high statistical probability of their emergence. Contemporary solutions frequently invoke sociological or self-destructive "Great Filters". This work does not attempt to provide a definitive resolution to the Fermi Paradox but rather proposes a thermodynamically constrained interpretative framework based on universal physical limits. Using the Earth-Sun system as a baseline model, a theoretical and analytical formalization is provided to demonstrate that the inevitable increase in stellar luminosity restricts the technological window of opportunity to a critical fraction of geological time, operating as an exogenous Great Filter. After mathematically analyzing the thermodynamic, kinetic and thermal unviability of a classical interstellar exodus via massive biospheric containers or generation ships, a Mathematical Model of the Civilizational Survival Factor (\Psi) is formulated. It is postulated that the optimal and energetically favorable resolution against the Stellar Death Clock is not interstellar dispersal but rather astronomical engineering through the controlled migration of the planetary orbit within the expanding habitable zone. The universe remains silent not due to biotic self-destruction but because mature civilizations optimize their resources by stabilizing their home systems, rendering massive galactic expansion highly inefficient.