  Thermal noise arising from mechanical dissipation in dielectric reflective
coatings is expected to critically limit the sensitivity of precision
measurement systems such as high-resolution optical spectroscopy, optical
frequency standards and future generations of interferometric gravitational
wave detectors. We present measurements of the effect of post-deposition heat
treatment on the temperature dependence of the mechanical dissipation in
ion-beam sputtered tantalum pentoxide between 11\,K and 300\,K. We find the
temperature dependence of the dissipation is strongly dependent on the
temperature at which the heat treatment was carried out, and we have identified
three dissipation peaks occurring at different heat treatment temperatures. At
temperatures below 200\,K, the magnitude of the loss was found to increase with
higher heat treatment temperatures, indicating that heat treatment is a
significant factor in determining the level of coating thermal noise.
