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This is only a crude estimate of the thermal conductivity of the plaster (derived in view of the very crude quality of the experimental data). Assuming that the heat loss rate at the far boundary is negligible (after water at the boundary has been been evaporated), and, based on the detailed heat transfer analysis presented in the following thread https://www.physicsforums.com/threads/time-taken-for-heat-transfer.921537/#post-5814526 (post # 14), the temperature difference between the two boundaries (during the main part of the heating) is approximated by:$$\Delta T=\frac{qH}{2k}$$where q is the heat flux, H is the thickness of the sheet, and k is the thermal conductivity. From the data on the plot, the temperature difference over the main part of the heating curve is approximately 200 C. Substituting the data values into this equation gives a rough value of 0.65 W/(m^2C) for the thermal conductivity.