Force–displacement curves have been obtained on two polystyrene samples, having different molecular weight, at various temperatures and probe rates using an atomic force microscope. The force–displacement curves have been analysed using a novel method, which extends continuum elastic contact theories also to the plastic deformations. The Young's modulus and the yielding force of the two polystyrene samples have been determined as a function of temperature and frequency. It was also possible to calculate the Williams–Landel–Ferry coefficients for measurements above the glass transition temperature, and the viscoelastic activation energy for measurements below the glass transition temperature using the Arrhenius equation. All the calculated coefficients were in very good agreement with the literature values. The measured quantities span a wide range of temperature (85°C) and frequency (eight decades) and the shifts of all the quantities calculated from force–displacement curves obey the Williams–Landel–Ferry and Arrhenius equation with the same parameters. Quantitative and qualitative comparison of the Young's modulus, of the stiffness in the plastic region and of the yielding force of the two polystyrene samples revealed different viscoelastic behaviour because of the variation in glass transition temperature of the two samples, due to their difference in the molecular weight.