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Two new analytical temperature solutions are reported on the viscous dissipation effect in a microchannel flow driven by an oscillating lower plate, an extension of Stokes's second problem. The methodology is solving the momentum and energy equations analytically, assuming Newtonian, one-dimensional, incompressible, laminar with constant properties. Although the velocity solution had long been obtained, only a time-averaged temperature solution had been available, until recently; when two full time-dependent temperature solutions were reported, for two symmetric temperature boundary conditions. The present work extends further with two more full solutions on asymmetric thermal conditions, namely, insulated on one oscillatory plate and isothermal on the other stationary plate, and vice-versa. Comparisons are also made with the previous two cases, and all four solutions are validated with numerical solutions. This fundamental study may have application to such a situation as the synovial flow in artificial hip-joints.