The structural and gas-sensitive properties of n-N SnO2/κ(ε)-Ga2O3:Sn heterostructures were investigated in detail for the first time. The κ(ε)-Ga2O3:Sn and SnO2 films were grown by the halide vapor phase epitaxy and the high-frequency magnetron sputtering, respectively. The gas sensor response and speed of operation of the structures under H2 exposure exceeded the corresponding values of single κ(ε)-Ga2O3:Sn and SnO2 films within the temperature range of 25–175 °C. Meanwhile, the investigated heterostructures demonstrated a low response to CO, NH3, and CH4 gases and a high response to NO2, even at low concentrations of 100 ppm. The current responses of the SnO2/κ(ε)-Ga2O3:Sn structure to 104 ppm of H2 and 100 ppm of NO2 were 30–47 arb. un. and 3.7 arb. un., correspondingly, at a temperature of 125 °C. The increase in the sensitivity of heterostructures at low temperatures is explained by a rise of the electron concentration and a change of a microrelief of the SnO2 film surface when depositing on κ(ε)-Ga2O3:Sn. The SnO2/κ(ε)-Ga2O3:Sn heterostructures, having high gas sensitivity over a wide operating temperature range, can find application in various fields.