I am trying to understand the extrapolation of enthalpy $\Delta H^{\ddagger}$ and entropy of activation $\Delta S^{\ddagger}$ from the Eyring equation. It's typically cast as:
$$\ln\left(\frac{k}{T}\right) = \frac{-\Delta H^{\ddagger}}{RT} + \frac{\Delta S^{\ddagger}}{R} + \ln\left(\frac{k_\mathrm{B}}{h}\right)$$
where $k$ is the rate, $T$ is the temperature, $R$ is the ideal gas constant, $k_\mathrm{B}$ is the Bolztmann constant, and $h$ is the Planck constant. However, the entropy itself also has a temperature dependence in principle (i.e. harmonic oscillator entropy is a function of temperature). Is there a way to determine the temperature dependence of the entropy of activation from the Eyring equation for a real experiment?