Double electron capture (DEC) is a rare nuclear decay process in which two orbital electrons are simultaneously captured in the same nucleus.
The measurement of its two-neutrino emitting mode (2$\nu$DEC) provides a new reference for the calculation of nuclear matrix elements, while the zero-neutrino emitting mode (0$\nu$DEC) would demonstrate a violation of lepton number conservation.
For $^{112}$Sn, the search for DEC to the excited state in ${}^{112}$Cd has been carried out using a High-Purity Germanium detector and a $^{112}$Sn enriched tin sample, but no significant signal has been observed so far.
2$\nu$DEC to the ground state in ${}^{112}$Cd has not been performed due to the self-absorption of X-rays and Auger electrons in the tin sample.

We propose a novel approach to search for the 2$\nu$DEC mode to the ground state in ${}^{112}$Cd using a $\gamma$-ray Transition Edge Sensors ($\gamma$-TESs) with tin absorbers.
The calorimetric approach in which the signal would be generated in the detector allows us to detect two X-ray or Auger electrons resulting from the ${}^{112}$Sn DEC with high energy resolution.
The future multi-pixel $\gamma$-TESs increase the target mass and thus the sensitivity.
In this proceedings, we demonstrate the 2$\nu$DEC search with this approach.
The preliminary results of our search for the ${}^{112}$Sn 2$\nu$DEC to the ground state in ${}^{112}$Cd with 90 hours, four $\gamma$-TESs data, and the future prospects are presented.