Phosphorylates thymidine and thymidine analogs, such as azidothymidine (AZT). Part of the salvage pathway for pyrimidine deoxyribonucleotide synthesis (By similarity). ATP + thymidine = ADP + dTMP + H(+) Homotetramer (By similarity). Two molecules of substrate bind to each enzyme tetramer. Belongs to the thymidine kinase family.