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Here we present the unusual dependence of magnetoimpedance effect on applied axial magnetic field for Finemet-type nanocrystalline wires in the low-temperature range between - 195degC to 200degC. The dependence exhibits two maxima, with a stronger maximum at the magnetic field value of the order of anisotropy, when applied in the direction of previous saturation. Such behavior is treated in terms of strong induced transversal magnetoelastic anisotropy due to the thermal expansion of the wire. The experiment is confirmed by a simple model which describes also the temperature dependence of the transversal magnetic anisotropy.