In this work, we use the transient time correlation function (TTCF) method to evaluate the response of a fluid confined in a nanopore and subjected to shear. The shear is induced by the movement of the boundaries in opposite directions and is made of moving atoms. The viscous heat generated inside the pore is removed by a thermostat applied exclusively to the atomic walls, so as to leave the dynamics of the fluid purely Newtonian. To establish a link with nonlinear response theory and apply the TTCF formalism, dissipation has to be generated inside the system. This dissipation is then time correlated with a phase variable of interest (e.g., pressure) to obtain its response. Until recently, TTCF has been applied to homogeneous fluids whose equations of motion were coupled to a mechanical field and a thermostat. In our system dissipation is generated by a boundary condition rather than a mechanical field, and we show how to apply TTCF to these realistic confined systems, comparing the shear stress response so obtained with that of homogeneous systems at equivalent state points.