(abridged) Methods: We derive maps of submillimeter dust optical depth and effective dust temperature from Herschel data that were calibrated against Planck. After calibration, we then fit a modified blackbody to the long-wavelength Herschel data, using the Planck-derived dust opacity spectral index beta, derived on scales of 30 (or ~1 pc). We use this model to make predictions of the submillimeter flux density at 850 micron, and we compare these in turn with APEX-Laboca observations. Results: A comparison of the submillimeter dust optical depth and near-infrared extinction data reveals evidence for an increased submillimeter dust opacity at high column densities, interpreted as an indication of grain growth in the inner parts of the core. Additionally, a comparison of the Herschel dust model and the Laboca data reveals that the frequency dependence of the submillimeter opacity, described by the spectral index beta, does not change. A single beta that is only slightly different from the Planck-derived value is sufficient to describe the data, beta=1.53+/-0.07. We apply a similar analysis to Barnard 68, a core with significantly lower column densities than FeSt 1-457, and we do not find evidence for grain growth but also a single beta. Conclusions: While we find evidence for grain growth from the dust opacity in FeSt 1-457, we find no evidence for significant variations in the dust opacity spectral index beta on scales 0.02<x<1 pc (or 36<x<30). The correction to the Planck-derived dust beta that we find in both cases is on the order of the measurement error, not including any systematic errors, and it would thus be reasonable to directly apply the dust beta from the Planck all-sky dust model. As a corollary, reliable effective temperature maps can be derived which would be otherwise affected by beta variations.
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