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Permalloy-based thin film structures are excellent materials for sensor applications. Temperature dependencies of the magnetic properties and giant magneto-impedance (GMI) were studied for Fe₁₉Ni₈₁-based multilayered structures obtained by the ion-plasma sputtering technique. Selected temperature interval of 25 °C to 50 °C corresponds to the temperature range of functionality of many devices, including magnetic biosensors. A (Cu/FeNi)₅/Cu/(Cu/FeNi)₅ multilayered structure with well-defined traverse magnetic anisotropy showed an increase in the GMI ratio for the total impedance and its real part with temperature increased. The maximum of the GMI of the total impedance ratio ΔZ/Z = 56% was observed at a frequency of 80 MHz, with a sensitivity of 18%/Oe, and the maximum GMI of the real part ΔR/R = 170% at a frequency of 10 MHz, with a sensitivity of 46%/Oe. As the magnetization and direct current electrical resistance vary very little with the temperature, the most probable mechanism of the unexpected increase of the GMI sensitivity is the stress relaxation mechanism associated with magnetoelastic anisotropy. © 2017 by the authors. Licensee MDPI, Basel, Switzerland.