The aim of this study was to perform precision measurements of the frequency-temperature dependences of the loss angle tangent of the liquid-solid composite with the FDS Dirana meter. The composite consisted of heavily moistered oil-impregnated pressboard. The moisturization of the pressboard occurred in a manner as close as possible to the process of wetting the insulation in power transformers to a moisture content of (5.0 ± 0.2) wt. %. This value of moisture content was chosen because exceeding this value can lead to transformer failure. The measuring temperature range was from 293.15 K (20 °C) to 333.15 K (60 °C), with a step of 8 K. The measuring frequency range was 0.0001 Hz to 5000 Hz. It was observed that the shape of the frequency dependence of the loss angle tangent for a moisture content of 5.0 wt. % does not depend on the value of the measuring temperature. An increase in temperature leads to a shift of the waveforms into the higher frequency region. This is associated with a decrease in the relaxation time, and its value depends on the activation energy. It was found that a good fit of the waveforms, simulated by Dirana, to the actual tgδ waveforms obtained at temperatures between 293.15 K (20 °C) and 333.15 K (60 °C) requires the introduction of temperatures, higher than the actual insulation temperatures, into the program. It was found that estimating the moisture content for different temperatures using Dirana soft-ware for insulating an oil-impregnated pressboard produced large discrepancies from the actual content. Better results were obtained after an adjustment requiring manual temperature correction towards higher, compared to measured, temperatures. The moisture content estimated after correction by the Dirana meter ranges from of 4.5 wt. % to 5.7 wt. % and increases almost linearly with increasing measuring temperature. The average moisture content estimated by the Dirana meter for all measuring temperatures is 5.1 wt. % and is close to the actual content (5.0 ± 0.2) wt. %. The uncertainty of the estimate is ±0.43 wt. % and is more than twice as high as the true value.