Corrosion under insulation (CUI) is a major risk factor for the material integrity of insulated equipment that is encountered i.a. in the chemical process industries. Undetected CUI has been the root cause for major accidents, including loss-of-site, loss-of-life, prolonged plant shutdown, and environmental pollution. Reducing CUI risk via labour-intensive inspection routines is associated with billions of dollars of annual maintenance costs worldwide. CUI is caused by water bypassing a weather shield, migrating through the insulation and contacting the equipment surface. The resulting corrosion rates are very high and the process is hidden from view. Surprisingly, the fundamental mechanisms that drive water migration through insulation have been largely unexplored. In this work we present novel experimental investigations of the evaporation and drying dynamics for a heated vertical pipe with preformed mineral wool insulation and metal cladding. Relative humidity and temperature sensors provide measurements of how the water evaporates and travels through the system during controlled water ingress experiments. The experimental data shows that the drying time of the insulation material is proportional to the amount of water added. We find that the drying process proceeds in two stages, where the length of the first drying regime is directly related to the diffusion-limited evaporation from the bulk liquid water, while the second drying time is influenced also by other factors such as the adsorption and desorption of water on the insulation material fibres. The findings have implications for how time of wetness, used in CUI risk-based inspection methods, can be obtained from humidity sensor data. The new insights into water transport in insulation enables a paradigm shift towards predictive CUI maintenance using humidity spot sensors.