Liquid hydrogen (LH2) has excellent properties such as large latent heat, low viscosity, and so on. Because of these properties, LH2 is expected to be used as a coolant for a high-critical-temperature superconductor (HTS), including MgB2. The over-critical-current properties of an HTS are important for the stable designs of HTS devices cooled by LH2; however, the temperature change of a sheathed superconducting wire cannot be revealed only by current-voltage properties beyond critical current, since the current-sharing ratio among MgB2 and sheath materials is not unknown. In this study, transient over-critical-current tests were performed on a short MgB2 sample cooled by LH2 under magnetic field, and the sample temperatures were calculated from test data. In addition, the test sample temperature based on the test was compared with that of the computer simulation result. It was found that the temperature change of the wire just after the transport current exceeds the critical current is affected by external magnetic fields.