required that is beyond the scope of this paper. For the latter, we will use the noise performance of the SPIDER TES bolometers, which begin to be dominated by $1/f$ at 0.1 Hz, as guide to what could be achieved with effort, since CMB experiments are quite sensitive to low frequency noise [@SPIDER] and thus we will set a design goal of $\omega_{S/N \, \delta \! P_{t}} > $ 0.5 hz.

TES Phase Separation {#sec:PhaseSep}
====================

Unfortunately, as first realized in the earliest days of CRESST calorimeter development [@CRESST_1995_ProbstModel], the simple 2 DOF block thermal model shown in Fig. \[fig:CaWO4\_Qdiag\] that we have used for our CRESST-II phonon-detector resolution estimates is not entirely accurate, since $G_{tb}$ is also significantly larger than the internal thermal conductance of the W TES, $G_{t\,int}$([*c*f.]{} Table. \[tab:PhononDet\]). In this situation, the difference in temperature between the TES $T_{c}$ and the effective bath temperature is mostly internal to the TES, and thus there is a significant temperature gradient across the sensor. In devices with large $\alpha$, this thermal gradient is further exasperated by positive-feedback effects of joule heating and the TES can separate into sharply defined superconducting and normal regions, with only a very thin region 