Nanoplllars of ferroelectric polymers are of strong interest for the fabrication of low-cost nanoscale actuators and memories of high density. However, a limiting factor of polymers compared to inorganic ferroelectric materials is their low ferro- to paraelectric Curie transition, a problem compounded by the possible further decrease of the Curie temperature in nanostructures as was suggested by previous studies. Here we develop a methodology based on piezoresponse force microscopy to study the thermal stability of data stored in free-standing poled and annealed nanopillars of ferroelectric poly(vinylidene fluoride-ran-trifluoroethylene), P(VDF-TrFE), and thereby demonstrate that the Curie transition of a properly processed strongly confined ferroelectric polymer is not significantly modified compared to the bulk material, at least attograms corresponding to ca. 1500 chains only.