Rail switch assembly having pairs of rails and a basis therefor, wherein each pair of rails comprises a fixed rail and a movable rail or switch tongue, wherein at regular intervals mounting plates/slide plates have been provided for supporting the rails and forming a slide surface for the switch tongues, wherein the rails each comprise a foot and a web extending upwards from the foot, wherein the foot has an upper surface and a lower surface and the web has a first side surface and a second side surface opposite thereto, comprising a heating means for at least one rail of at least one pair of rails, for instance a heating element extending alongside it that has been placed against one or more of the said surfaces, wherein of said pair of rails at least one of both rails has been provided with a first body of thermally insulating material, that has been arranged against at least a part of the lower surface of the foot of said rail and in longitudinal direction extends at least partially between the mounting plates/slide plates for said rail.