all of the devices tested, Eq. (\[eq:ThermalFlux\]) was fitted to data of this kind under the assumption that the temperature of the TES was maintained constant at nearly $T_C$, which is true for sufficiently sharp transitions. $K$, $n$ and $T_C$ were free parameters in the fitting process, with $T_C$ corresponding to the intercept of the curve on the $P_{B}=0$ axis.

![\[fig:PT\_Inset\_PV\] (a) Power against voltage across the TES, $V_{TES}$, for device 3R$_b$, for a subset of $T_B$ from $T_{B0}=67.5$mK to 125mK from top to bottom. (b) Net power flow from the TES island to the heat bath, $P_{B}$, against bath temperature, $T_B$, for devices 3IC (green, solid), 3I$_b$ (red, dashed) and 3R$_b$ (magenta, compound dashed). Points show measured data, and lines indicate model fits according to Eq. (\[eq:ThermalFlux\]). ](Figure4.pdf){width="3.37in"}

For each device, the measured power at the lowest bath temperature, $T_{B0} = 68 \pm 1$mK, was used to calculate the normalised power per leg, $\epsilon$, according to Eq. \[eq:Epsilon\]. In this way, the measured fluxes were normalised to the theoretical ballistic power for a device with straight legs with termination temperatures $T_{B0}$ and $T_C$. The total thermal conductance $G$ of the support structure was determined from Eq. \[eq:ThermalCond\]. Table \[tab:TES\_Props\] 