A high-quality smart filter for terahertz range with relative tunability reaching 20% has been demonstrated. The filter is based on a narrow transmission band, which originates from a defect mode that appears due to insertion of a single crystal of KTaO3 into otherwise periodic one-dimensional photonic crystal. Frequencies of defect modes are controlled by the refractive index of the defect: their high tunability is achieved by the strong temperature dependence of the dielectric properties of KTaO3. The low losses of KTaO3 lead to a high peak transmission of the filter. Influence of the defect losses on the properties of the filter is also discussed.