We investigate the shear surface rheology of a thermosensitive polymer, PNIPAM (poly(N isopropylacrylamide)), adsorbed at the air water interface using an interfacial stress rheometer. This polymer is characterized by a lower critical solution temperature, LCST, of 32 C; i.e., PNIPAM chains undergo a coil to globule transition as the temperature is increased above the LCST. We measure a spectacular increase in the surface shear elasticity and viscosity of PNIPAM layers as a function of the temperature around the LCST due to an increase in the amount of adsorbed species as the solvent quality decreases for PNIPAM chains. Moreover, the layers undergo a transition from a Newtonian liquidlike state to an elastic state due to an increase in intermolecular entanglements. We also show that the heating protocols have a strong influence on the rheological properties of the layers. In particular, we show that when the solutions are continuously heated from ambient temperature to well above the LCST, PNIPAM chains can be trapped in a nonequilibrium state at the aira??water interface above the LCST. Last, we report on the influence that the PNIPAM bulk concentration and molecular mass have on the surface rheological properties at the aira??water interface.