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+). ATP + dTMP = ADP + dTDP Pyrimidine metabolism; dTTP biosynthesis. Homodimer. The levels of dTMP kinase mRNA and its enzymatic activity fluctuate during the cell cycle, peaking at the S phase. Belongs to the thymidylate kinase family.