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We present an experimental demonstration of passive, dynamic thermal regulation in a solid-state system with temperature-dependent thermal emissivity switching. We achieve this effect using a multilayered device, comprised of a vanadium dioxide (VO2) thin film on a silicon substrate with a gold back reflector. We experimentally characterize the optical properties of the VO2 film and use the results to optimize device design. Using a calibrated, transient calorimetry experiment we directly measure the temperature fluctuations arising from a time-varying heat load. Under laboratory conditions, we find that the device regulates temperature better than a constant emissivity sample. We use the experimental results to validate our thermal model, which can be used to predict device performance under the conditions of outer space. In this limit, thermal fluctuations are halved with reference to a constant-emissivity sample.