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When modeling systems made up of two materials with different thermodynamic properties, a physical interface can be introduced to account for the border where the materials meet. This interface separates our model’s standard grid into two regions, each with its unique physical properties. At these interfaces, boundary conditions can be imposed to represent the difference in heat and in heat flux between the different materials so that their interaction may be modeled accurately. Because standard finite difference methods are inadequate to deal with interfaces, a Matched Interface and Boundary (MIB) technique is investigated in this work to solve the heat equation with interfaces. MIB techniques are powerful tools used to solve partial differential equations due to their efficiency and stability. Without loss of generality, this work will solve 1-dimensional interface problems to demonstrate the accuracy and computational efficiency of this method, which will create a linear system of equations to be solved at each step in time throughout the duration of the model.