Pressure gain combustors (PGCs) have demonstrated significant advantages over conventional combustors in gas turbine engines by increasing the thermal efficiency and reducing the pollution emission level. PGCs use shock waves to transfer energy which contributes to the increase in outlet total pressure. One of the major obstacles in the actual implementation of PGCs in the gas turbine cycle is the exploitation of the highly unsteady flow of the combustor outlet with the downstream turbine. Because of the higher outlet temperature from the PGCs, the turbine blade cooling becomes essential. Due to the highly fluctuating unsteady flow of PGCs, 3D CFD simulation of turbines becomes very expensive. In this work, an alternative approach of using a 1D unsteady Euler model for the turbine is proposed. One of the novel aspects of this paper is to implement the turbine blade cooling in the unsteady 1D Euler model. The main parameters required for the turbine blade cooling are the cooling air mass flow rate, temperature, and pressure. Due to the introduction of coolant flow, the blades are no longer adiabatic and the mass flow rate across the turbine is not constant. Comparing the 1D Euler results against zero-dimensional calculation and 3D CFD approach showed a very good match for both steady and unsteady simulations confirming the applicability of the 1D method.