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This article discusses an express control method that allows in situ measurements of the thermal conductivity of insulation materials. Three samples of the most common thermal insulation materials, such as polyurethane, extruded polystyrene, and expanded polystyrene, were studied. Additionally, optical and organic glasses were investigated as materials with a stable value of thermal conductivity. For the measurement of thermal conductivity, the express control device, which implements the differential method of local heat influence, was used. The case studies were focused on the reduction of fluctuations of the measured signals caused by different influencing factors using wavelet transform. The application of wavelet transform for data processing decreased the thermal conductivity measurement’s relative error for organic glass SOL and optical glasses TF-1 and LK-5. The application of wavelet transform thermal conductivity measurement data for polyurethane, extruded polystyrene, and expanded polystyrene allowed to reduce twice the duration of express control while maintaining the same level of measurement error. The results of the investigation could be used to increase the accuracy in express control of the thermal conductivity of insulation materials by improving the data processing. This approach could be implemented in software and does not require a change in the design of the measuring equipment or the use of additional tools.