using a two-stage SQUID amplifier as a low-noise current-to-voltage converter. The TES and SQUID chips were mounted in an optically blackened light-tight box and cooled to a base temperature of 68mK in an adiabatic demagnetisation refrigerator (ADR). The bath temperature of the TES chip was taken to be that of the copper housing, held constant to within 200$\mu$K by means of the residual current in the ADR magnet. Current and voltage offsets and stray resistances were identified and compensated for in data processing. The TES current response to a step in voltage was obtained by biasing the TES in its transition and superimposing a square wave on the bias input, with small amplitude compared to the voltage width of the transition. Current response was averaged over multiple leading-edge voltage steps.

Results and Discussion {#sec:Results_Discussion}
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A TES voltage-biased within its transition self-regulates its temperature due to negative electrothermal feedback. In the steady state, $dT / dt= 0$, the net power flow from the island to the heat bath is equal to the Joule power dissipated in the bilayer. The power flow is therefore given by $P_{B} = P_{J} = IV_{TES}$, allowing $P_{B}$ to be obtained from a series of $I$-$V_{TES}$ 