  Coherent elastic neutrino-nucleus scattering (CE$\nu$NS) offers a valuable
approach in searching for physics beyond the Standard Model. The Ricochet
experiment aims to perform a precision measurement of the CE$\nu$NS spectrum at
the Institut Laue-Langevin nuclear reactor with cryogenic solid-state
detectors. The experiment plans to employ an array of cryogenic thermal
detectors, each with a mass around 30 g and an energy threshold of sub-100 eV.
The array includes nine detectors read out by Transition-Edge Sensors (TES).
These TES based detectors will also serve as demonstrators for future neutrino
experiments with thousands of detectors. In this article we present an update
in the characterization and modeling of a prototype TES detector.
