With emphasis on thermal losses from internally heated equipment in process applications, the results of conjugate heat and mass transfer modeling are presented for a category of Stefan flow involving vaporization in a semi-permeable heterogeneous media. The model simulates the initial stages of the drying process for wet, partially saturated insulation material abutting heated equipment. Dimensionless forms of the governing equations constitute the model basis for a transient, one-dimensional problem abstraction. Numerical solutions are obtained using finite-difference techniques. Model results are presented to demonstrate drying rate variation at high heat rates in the materials of interest to the applications. Summary results include drying rate, saturation distribution, and fluid velocity profiles with comparison of observed drying front penetration depth to existing literature.