Catalyzes the phosphorylation of 2-phosphoglycerate to 2,3-diphosphoglycerate. Involved in the biosynthesis of cyclic 2,3-bisphosphoglycerate, a thermoprotectant. (2R)-2-phosphoglycerate + ATP = (2R)-2,3-bisphosphoglycerate + ADP + H(+) Thermoadapter biosynthesis; cyclic 2,3-diphosphoglycerate biosynthesis; cyclic 2,3-diphosphoglycerate from 2-phospho-D-glycerate: step 1/2. Belongs to the 2-phosphoglycerate kinase family.