Catalyzes the phosphorylation of thymidine monophosphate (dTMP) to thymidine diphosphate (dTDP), the immediate precursor for the DNA building block dTTP, with ATP as the preferred phosphoryl donor in the presence of Mg(2+). {ECO:0000269|PubMed:12614151, ECO:0000269|PubMed:2017365, ECO:0000269|PubMed:34918187, ECO:0000269|PubMed:8024690, ECO:0000305|PubMed:18469}. This is the function of Ensembl gene identifier ENSG00000168393 (DTYMK, deoxythymidylate kinase).