In middle and northern Europe many existing buildings have to be improved energetically by means of additional thermal insulation on the building envelope. For buildings with façades worthy to be preserved, only an inside insulation layer may be possible, but with inside insulation layers, moisture problems often arise. Using a capillary active material, as has been done in this research, the amount of condensation water on the cold side of the inside insulation can be reduced. Also, a vapor retarder is not necessary and, therefore, the drying potential is not limited. Based on the physical models for coupled heat, air, water vapor, capillary water, pollutant, and salt transport (CHAMPS) in porous building and insulating materials and the computer code DELPHIN developed at the Institut für Bauklimatik (Dresden, Germany), in continuation of the topic “capillary active inside insulation,” further substances and substance combinations were investigated in order to develop safe wall constructions in connection with appropriate thermal insulation. That was done via a computational prognosis and, secondly, with practical application in six test houses in Germany. The latter were connected to measurements of all climatic boundary conditions, such as temperature, relative humidity, shortwave radiation, precipitation, wind velocity and direction, as well as hygrothermic properties, such as temperature and humidity, in the materials. For numerical simulation, a set of storage and transport functions for the porous building materials is necessary. This paper describes the modeling and measurement of the moisture storage and moisture transport functions for the capillary active insulation material “calciumsilicate” used in the study. A comparison of measured and calculated hygrothermic performance within the envelope in a renovated frame house near Hannover, Germany, shows good correspondence. Heat losses have been reduced to one-third, and condensation water does not exceed 0.5 kg/m² during winter. Moreover, a simplified computer code, COND, has been developed. It delivers about the same results and a sufficient assessment of the moisture distribution in the structure.