When sheared sufficiently strongly, suspensions having a large volume fraction of solid particles can exhibit a dramatic increase in viscosity (shear thickening) and even solidify (shear jamming). Investigations to date have almost exclusively focused on rigid, non-responsive particles, which do not allow in situ tuning of shear thickening or jamming. Here we report suspensions of polymeric micron-sized particles with accessible glass transition temperatures Tg) designed to control their non-Newtonian rheology. The underlying mechanical stiffness and interparticle friction between particles change dramatically near Tg. We capitalize on these properties and show that, in contrast to conventional systems, a dramatic and non-monotonic change in shear thickening is observed as the suspensions transition through the particles’ Tg. This behavior enables the in situ turning on or off of shear jamming by varying the temperature relative to Tg, and lays the groundwork for thermally switchable jamming systems.