The c-axis thermal conductivity of a Sb2Te3 nanowire is measured using the scanning thermal microscopy technique within the 3ω mode. The contact parameters, in terms of boundary contact resistance and contact area radius, are measured in specific configurations, and the values found are assumed not to vary within the nanowire case. The method does not require handling or suspending the nanowire. The measured thermal conductivity at room temperature is found to be in a good agreement with that of the bulk, since the nanowire characteristic dimension in the diffusion direction is larger than the phonon mean free path.