Aviation-induced contrail cirrus is known to be responsible for significant climate impact, yet fuel and engine-based mitigation strategies receive less emphasis than flight path and altitude optimization research. Flight path optimization studies require an enormous amount of multiparty coordination, real-time data collection, and resource-rich research partners. This study assesses the impact of sustainable aviation fuels (SAFs) on contrail formation, which is a research avenue more amenable to modeling. The usage of three SAF types, Hydroprocessed Esters and Fatty Acids Synthetic Paraffinic Kerosene (HEFA-SPK), Fischer-Tropsch Synthetic Paraffinic Kerosene (FT-SPK), and Alcohol-to-Jet Synthetic Paraffinic Kerosene (ATJ-SPK), was modeled on four representative flight routes. A mathematical framework based on the Schmidt-Appleman criterion (SAC) was developed to evaluate spatially resolved contrail formation potential along great circle routes. In this framework , the parameter G represents the slope of the exhaust-air mixing line in temperature-humidity space and directly controls the critical ambient temperature threshold for contrail formation. All three SAFs produced a marginal increase in mean contrail formation potential relative to baseline kerosene across all routes. This result is attributed to the higher water vapor emission indices and specific combustion heat of SAFs, which increase the slope parameter G and shift the threshold temperatures toward warmer values. However, this thermodynamic effect operates independently of the primary mitigatory mechanism of SAFs: the reduction of non-volatile particulate matter (nvPM) emissions. The reduced nvPM emissions suppress ice crystal nucleation through a distinct physical pathway not captured within the thermodynamic framework. The results therefore represent a thermodynamic formation potential only, and the full climate benefit of SAF deployment is expected to be realized when nvPM effects are incorporated alongside the thermodynamic assessment presented here.