The TORIO-229 experiment aims for a direct model-independent determination of the transition energy of 229 m Th produced in 233 U alpha decay. This knowledge will be of interest for the development of a scientific clock exploiting the thorium isomeric state, which would be able to significantly surpass the precision of the presently best clocks. As a detector for the isomeric transition, it is planned to use an array of fast transition-edge sensors (TESs) which demonstrated to be feasible in our previous work where the Ir/Au TES prototype demonstrated 4.6 ± 1.7  µs rise time, 5.8 ± 2.1  µs fall time and 0.789 ± 0.023  eV energy resolution and signal-to-noise ratio of ∼ 10 with one-photon (2.824 eV) signal, satisfying the experimental requirements. Such a microcalorimeter will allow to register the transition in every possible channel in the energy range from 3 to 50 eV and with a lifetime of > 5 µs. To have a full characterization of a single TES for the final detector array design, its thermal conductance has to be measured. In this contribution, we report on a test measurement of thermal coupling of a TORIO-229 prototype-like iridium-gold TES.