Methods and apparatus for maintaining the thermal equilibrium of a substrate and an immersion lithographic apparatus are disclosed using or having a timetable comprising information regarding the position, speed and/or acceleration of the substrate; and an evaporation controller and/or condensation controller acting to decrease localized evaporation and/or increase localized condensation in response to the information in the timetable. Evaporation of liquid from the surface of the substrate cools it down, while condensing liquid on its bottom surface heats the substrate locally.