We found that a high-mobility semimetal 1Tʹ-MoTe2 shows a significant pressure-dependent change in the cryogenic thermopower in the vicinity of the critical pressure, where the polar structural transition disappears. With the application of a high pressure of 0.75 GPa, while the resistivity becomes as low as 10 µΩcm, thermopower reached the maximum value of 60 µVK −1 at 25 K, leading to a giant thermoelectric power factor of 300 µWK −2 cm −1 . Based on semi-quantitative analyses, the origin of this behavior is discussed in terms of inelastic electron-phonon scattering enhanced by the softening of zone-center phonon modes associated with the polar structural instability.Enhancement of thermoelectric effects at low temperatures is demanded for the development of cryogenic Peltier coolers. From the viewpoint of the power output of these devices, it is necessary to find the material with high power factor (= S 2 ρ -1 ), where S and ρ denote thermopower and resistivity, respectively. In the cryogenic temperatures below 50 K, strongly correlated electron systems such as cobalt oxides and heavy-fermion compounds [1-5] were found to show much larger power factors than those for high-mobility semiconductors and semimetals typified by Bi2Te3 (see Fig. 4) [6][7][8][9][10].Since thermopower is the measure of the entropy normalized per charge carrier, the unusually high power factors originated from the high thermopower in these compounds were discussed in terms of the large entropy of spin and orbital degrees of freedom.As well as the spin and orbital entropy, the phonon entropy has a potential for the enhancement of thermopower through electron-phonon scattering [11,12]. A typical example is the phonon-drag effect observed in the clean system with long mean free path phonons [12]. However, since the enhancement of thermopower through the phonon-drag effect requires a high thermal conductivity κ,