The partition of temperature between electrons and ions across Earth's bow shock is a long-standing problem in modeling particle entry into the magnetosphere. Observations have shown that the ion temperature increase across collisionless, fast mode shocks (as in Earth's bow shock) is substantially larger than that of the electrons. A model that can quantitatively explain this result will provide a better understanding of the relationships between collisionless shock parameters and particle behavior across the shock layer, finding applications to multifluid models of particle entry to the Earth's magnetosphere, as in the polar rain. In this paper we present a model that quantitatively determines the partition of temperature between the electrons and ions across the shock. The model couples a simplified Vlasov guiding center ordered electron fluid problem with the Rankine-Hugoniot conservation equations to determine the downstream partition of electron and ion temperature given a few observational constraints. We work in the deHoffmann-Teller reference Frame (HTF) because in HTF the electrons are only coupled to the ions through the electrostatic potential. This approach does not preclude the subsequent secondary thermalization of the ions by means of wave-particle interactions. We demonstrate under this approximation that the model recovers the electron temperature jumps of a new ISEE 1 database of 129 Earth bow shock crossings developed and analyzed by Hull et al. [2000>. The model also recovers trends in the downstream ion temperature at shocks observed by ISEE 1 previously cataloged by Thomsen et al. [1987>. ¿ 2000 American Geophysical Union