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. Very low mRNA levels in the quiescent cells. As cells exit from G0 to G1 phase, the expression levels gradually increase. Belongs to the thymidylate kinase family.