Phosphorylates thymidine, deoxycytidine, and deoxyuridine in the mitochondrial matrix (PubMed:11023833). In non-replicating cells, where cytosolic dNTP synthesis is down-regulated, mtDNA synthesis depends solely on TK2 and DGUOK (By similarity). ATP + thymidine = ADP + dTMP + H(+) 2'-deoxycytidine + ATP = ADP + dCMP + H(+) 2'-deoxyuridine + ATP = ADP + dUMP + H(+) Homodimer. Found in most tissues; highly expressed in liver. Belongs to the DCK/DGK family.