This work studies the stress in stimuli-responsive planar polymer brushes of neutral water-soluble polymers with low to very high graft densities using strong stretching theory (SST). SST with the Langevin force-extension relation for a polymer chain is extended to the study of stimuli-responsive brushes. The stress profile and other structural properties of a poly(N-isopropylacrylamide) (PNIPAm) brush are then obtained using the extended SST and an empirical Flory-Huggins parameter. The swelling ratio predicted by our model is in good qualitative agreement with experimental measurements from the literature. Our model predicts that the stress in a PNIPAm brush is inhomogeneous and compressive at all temperatures and graft densities. The resultant stress is predicted to increase in magnitude with increasing graft density. A temperature increase results in a decrease in the resultant stress magnitude in low graft density brushes but a mild increase in high density brushes. This contrasting behavior arises from the minimum in the interaction free energy density versus polymer volume fraction curve for a PNIPAm solution at a large volume fraction and the stiffening of chains due to finite extensibility. Our results indicate that the ability to tune the resultant stress by changing the temperature diminishes with increasing graft density.