The process in which a relatively unspecialized cell acquires the specialized features of a DN2 thymocyte. A DN2 thymocyte is a CD4-,CD8- thymocyte that is also CD44+,CD25-. [ GOC:TermGenie GOC:dph http://purl.obolibrary.org/obo/go/references/0000086 http://www.ncbi.nlm.nih.gov/pubmed/25398325 ]