The present invention relates to methods and devices for maintaining the thermal equilibrium of a substrate and an immersion lithographic apparatus by having a timetable containing information regarding the position, speed and acceleration of the substrate; and an evaporation controller or condensation controller acting to decrease localized evaporation and/or increase localized condensation in response to the information in the timetable. Evaporation of water from the surface of the substrate cools it down, while condensing water on its bottom surface heats the substrate locally.