Thermoresponsive graft copolymers of N-isopropylacrylamide with polylactide (P(NIPAM-g-PLA)) are promising materials for the preparation of cell supports in cell sheet technology. Here, we studied the thermal behavior of thin and thick films prepared by spin-coating from P(NIPAM-g-PLA) (fresh and stored for 1 year), using atomic force microscopy. P(NIPAM-g-PLA) copolymers of different molecular weights were synthesized. The films’ swelling, Young’s moduli and roughness were tracked when lowering the temperature to that of the phase transition. The obtained thermal dependencies demonstrated that, in contrast to neat PNIPAM films, the prepared films efficiently dissolved at the temperature corresponding to the LCST of the copolymer in a solution. After a year of storage in ambient conditions, certain signs of polymer deterioration due to water uptake were observed. The obtained data on the phase transition in thin films of P(NIPAM-g-PLA) are of importance for their potential use as cell supports in the cell sheet technology.