In this study, we present a comprehensive thermo-optic characterization of an on-chip thin-film lithium niobate asymmetric Mach-Zehnder interferometer (aMZI) across a temperature range from 290 K to 10 K. We observe that the spectral shift of the aMZI is closely associated with changes in the environmental temperature. We experimentally observed a 4.88 nm wavelength shift of the aMZI from 290 K to 10 K. Moreover, the shift diminishes gradually below 50 K. Our observations highlight a distinctive non-linear temperature sensitivity, particularly pronounced at cryogenic temperatures. The high-resolution setup revealed a thermo-optic coefficient as low as 5.29 × 10-8 K-1 at 10 K. The presented results provide new practical guidelines for designing photonic circuits for applications in cryogenic optoelectronics.