may be derived from the coupled differential equations that describe the TES electrical and thermal circuits. Figure \[fig:Circuits\](a) shows a Thévenin-equivalent representation of a bias circuit connected to a TES having a current and temperature dependent resistance $R(T,I)$, where the current is read out using an inductively coupled SQUID circuit. $R_L$ is the sum of the bias and stray resistances, and $L$ represents the input inductance of the SQUID and any additional stray inductance due to wiring. Figure \[fig:Circuits\](b) shows a representation of the thermal circuit, where to a first approximation, the TES has a single heat capacity, $C$, coupled to the heat bath via support legs with thermal conductance, $G$. The differential electrical and thermal equations are then $$L \frac{\mathrm{d}I}{\mathrm{d}t} = V-IR_L-IR(T,I),$$ and $$C \frac{\mathrm{d}T}{\mathrm{d}t} = -P_B+P_J,$$ respectively. $T$ is the temperature of the central island, $P_B$ is the power flow to the heat bath, and $P_J= I^{2} R(T,I)$ is the Joule power dissipated in the TES bilayer. Notice that we distinguish between $T_{C}$, which is the critical temperature of the bilayer defined by some point on the superconducting transition, and $T$, which is the temperature of the bilayer as the instantaneous operating point moves up and down the 