We report a model that can be used to calculate superconducting transition temperature of a transition-edge sensor (TES), which is either a normal metal-superconductor-normal metal trilayer or a normal metal-superconductor bilayer. The model allows the T-{C} estimation of a trilayer when the normal metals at the bottom and at the top are different. Furthermore, the model includes the spin flip time of the normal metals. We use the T-{C} calculations from this model for selected Ir-based trilayers and bilayers to help understand potential designs of low T-{C} TESs. A Au/Ir/Au trilayer can have a low T-{C} because the superconducting order parameter is reduced with normal metals at both sides. On the other hand, an Ir/Pt bilayer can have a low T-{C} because the much larger electron density of states of Pt reduces the superconducting order parameter more effectively. Moreover, the spin flip scattering of paramagnetic Pt also contributes to the T-{C} reduction.