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The problem of unsteady oscillatory flow and heat transfer of porous me-dia sandwiched between viscous fluids has been considered through a horizontal channelwith isothermal wall temperatures. The flow in the porous medium is modeled using theBrinkman equation. The governing partial differential equations are transformed to ordi-nary differential equations by collecting the non-periodic and periodic terms. Closed-form solutions for each region are found after applying the boundary and interface conditions. The influence of physical parameters, such as the porous parameter, the frequency pa-rameter, the periodic frequency parameter, the viscosity ratios, the conductivity ratios, and the Prandtl number, on the velocity and temperature fields is computed numerically and presented graphically. In addition, the numerical values of the Nusselt number at the top and bottom walls are derived and tabulated.