The thermal diffusivity and effective infrared emissivity of water-methanol mixtures were measured at atmospheric pressure and ambient temperature using a pyroelectric thermal-wave resonator cavity. The applied frequency-scan method allows keeping the cavity length fixed, which eliminates instrumental errors and substantially improves the precision and accuracy of the measurements. A theoretical model describing conduction and radiation heat transfer in the cavity was developed. The model predictions and the frequency-scan experimental data were compared, showing excellent agreement. The measurements were performed for methanol volume fractions of 0, 0.5, 1, 2, 5, 10, 20, 40, 75, and 100%. The fitted thermal diffusivity and effective emissivity vs. concentration results of the mixtures were compared to literature theoretical and experimental data. The maximum resolution of 0.5% by volume of methanol in water by means of the thermal-wave cavity method is the highest reported to date using thermophysical techniques. Semi-empirical expressions for the mixture thermal diffusivity and infrared emissivity as functions of methanol concentration have been introduced. The expression for infrared emissivity is consistent with the physical principle of detailed balance (Kirchhoff's law). The expression for thermal diffusivity was found to describe the data satisfactorily over the entire methanol volume-fraction range.