As an example of a polymer with a lower critical solution temperature, T-LC, in water, we studied the phase behavior of a poly(N-isopropylacrylamide) copolymer. To adsorb it to a negatively charged surface, eve introduced a positively charged comonomer. The combination of direct force measurements with the surface forces apparatus (SFA) and contact angle measurements reveal a lower T-LC of the adsorbed layer than in bulk solution. At and above T-LC the adsorbed polymer chains collapse and the adsorbed layers on the two opposing surfaces attract each other. The resulting adhesion is strongly dependent on the applied speed of separation, emphasizing the role of slow molecular relaxations and rearrangements above T-LC The results also point to the validity of the time-temperature superposition principle to this polymer system at T > T-LC : at a low speed of separation the polymer layer is "liquid-like", and at high speeds its behavior is more "solid-like".