We report on the thermal stability of nonvolatile memory characteristics in an organic ferroelectric field-effect transistor (OFeFET) with a ferroelectric polymer of poly(vinylidene fluoride-trifluoroethylene)[P(VDF-TrFE)]. Pentacene-based OFeFETs are thermally annealed to understand how the thermal treatment affects nonvolatile memory characteristics. As increasing the annealing temperature up to 80 degrees C, both the memory window and the memory on-off ratio show no significant difference, while the memory properties results in rather monotonic reduction for beyond 80 degrees C which corresponds to the phase transition temperature of P(VDF-TrFE) molecules. It was found that the phase transition of the P(VDF-TrFE) from ferroelectric beta-phase to paraelectric gamma-phase at Curie's temperature plays a critical role for tailoring the electric characteristics in OFeFETs.