Assessing the potential for geothermal energy and liquid water presence in the Martian subsurface is crucial for future exploration and habitability studies. In this work, we employed comprehensive finite element model simulations adapted specifically for Martian conditions to estimate subsurface temperatures and the potential for liquid water at depth within Martian crater basins. Rock and fluid property values for basin fill were carefully adjusted to match Martian gravity, radiogenic heat generation, and compositional characteristics derived from rover analyses, Martian meteorite samples, and orbital spectroscopy data. Multiple modeling scenarios were explored to systematically evaluate end-member cases across critical variables such as heat flow, lithological composition, and average surface temperature. Sensitivity testing revealed that heat flow and average annual surface temperatures are the most important variables. Results were used in calculations based on a database of Martian craters to estimate the temperature of crater fill at depth. Our model results indicate significant potential for sustained liquid water in the subsurface within sedimentary deposits across a range of crater sizes and latitudes. They further suggest that viable geothermal reservoirs likely exist and are potentially accessible for future Martian missions seeking energy sources or exploring astrobiological hypotheses. This study provides a methodological framework for geothermal and hydrological assessments for the subsurface of Mars, contributing to ongoing planetary exploration strategies.