A memory device with a thin heater forms a programmable resistive change region in a sub-lithographic pillar of programmable resistive change material (“memory material”), where the heater is formed within the pillar between the top electrode and the programmable material. The device includes a dielectric material layer and vertically separated top and bottom electrodes having mutually opposed contact surfaces. A sub-lithographic pillar of memory material, which in a particular embodiment is a chalcogenide, is encased within the dielectric material layer. A heater between the pillar of programmable resistive material and the top electrode forms an active region, or programmable resistive change region, next to the heater when the memory device is programmed or reset.