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In contemporary cosmic microwave background experiments, bolometric detectors are often background limited, and in this case the sensitivity of instruments can only be improved by increasing the number of background-limited detectors, and so contemporary TES receivers contain as many pixels as possible. Frequency-domain multiplexing (fMUX) is one strategy for reading out many detectors with one SQUID. For any readout system, it is important to carefully evaluate the thermal design of detector, in conjunction with the readout bandwidth, in order to ensure stable electro-thermal feedback (ETF). We demonstrate a novel technique for characterizing the thermal circuit of our detectors, using am AC-bias and the fMUX electronics. This technique is used to study the internal thermal coupling of a TES bolometer. We illustrate how the insights gathered by this technique have been instrumental in improving the stability of our multiplexed detectors for the south pole telescope (SPT).