A thermally-assisted magnetic writing device includes at least one magnetic element including: a reference layer having a stable vortex magnetization configuration; a device to create a magnetic field to reversibly move the vortex core in the plane of the reference layer; a storage layer having a variable magnetization configuration; a non-magnetic spacer that separates and magnetically decouples the reference layer and the storage layer; an antiferromagnetic pinning layer in contact with the storage layer, the antiferromagnetic layer being capable of pinning the magnetization configuration of the storage layer, the storage layer having at least two storage levels corresponding to two pinned magnetization configurations; a device to heat the antiferromagnetic pinning layer such that when heated, the temperature of the antiferromagnetic pinning layer exceeds its blocking temperature such that the magnetization configuration of the storage layer is no longer pinned when warm.