A quasi-1D conjugate reduced order model (ROM) is developed to capture aero-thermal physics of effusion cooling in turbine airfoils. This framework explicitly considers the coolant supply from the leading edge and its distribution to both suction and pressure sides, the internal boundary layer flow between the shell and the inner core, the hole flow, the conduction on the solid walls, as well as the external film coverage. The solid temperature is allowed to vary both in metal shell thickness and the streamwise directions. Empirical correlations are employed to model pressure loss and heat transfer in the internal sections. Compound effect of multiple effusion cooling rows are utilized to capture cooling effectiveness and the heat load. Influence of mainstream static pressure, varying blowing ratios, hole’s diameter, hole’s pitch, coolant total pressure, and total temperature distributions along streamwise direction are taken into account. In Part I, the development and validation of the model is presented, which is shown to be capable of capturing complex internal aero-thermal physics of a turbine airfoil. Film coverage capability is separately validated successfully against available flat plate experimental data, with one case including internal channel and metal conduction. In Part II of this work, effusion cooling configuration is applied over an entire micro turbine vane and an exemplary optimization is carried out in the design space to minimize coolant flow while retaining metal temperature and its gradient below some limits. It is shown in the two-part work that the developed model is suitable for parametric studies of single-wall effusion turbine cooling such that comparative accuracy is obtained at a computational time 105 times lower than computational fluid dynamics (CFD) on a whole turbine vane/blade. Together, these two papers are intended to present, validate, and optimize the ROM for skin cooling in turbine airfoils by single-wall effusion.