In this article we demonstrate that concentrated p-NIPA suspensions in a low temperature glassy state can liquefy and then solidify again as the temperature is raised across the LCST. Our system exhibits all the typical behavior of disordered colloidal suspensions, but the behavior is controlled by temperature. Below the LCST it shows the behavior typical of a colloidal glass, near the LCST it behaves like a liquid, while above the LCST it exhibits the properties typical of a colloidal gel. Moreover, we show that the elasticity of these suspensions exhibits critical-like behavior as a function of temperature both above and below the LCST, with a critical temperature that corresponds to the LCST. Our results thereby suggest interesting analogies between the glass and gel phases of these thermosensitive microgel particles.