Generation of a long process of a CNS neuron, that carries efferent (outgoing) action potentials from the cell body in the spinal cord towards target cells in the thalamus. This axonal process is a member of those that make up the spinothalamic tract, one of the major routes of nociceptive signaling. [ GOC:cls GOC:jid GOC:dgh GOC:dph http://purl.obolibrary.org/obo/go/references/0000021 ]