Catalyzes the phosphorylation of (R)-mevalonate (MVA) to (R)-mevalonate 5-phosphate (MVAP). Functions in the mevalonate (MVA) pathway leading to isopentenyl diphosphate (IPP), a key precursor for the biosynthesis of isoprenoid compounds such as archaeal membrane lipids. (R)-mevalonate + ATP = (R)-5-phosphomevalonate + ADP + H(+) Farnesyl- and geranyl-pyrophosphates are competitive inhibitors. Slightly inhibited by high concentration of ATP. Optimum pH is 8.0-8.5. Exhibits at least 60% of its optimal activity over a rather broad pH range, from 5 to 7. Optimum temperature is 70-75 degrees Celsius. Highly thermostable. Retains 100% of its activity after 24 hours of incubation at 70 degrees Celsius. At 90 and 100 degrees Celsius, the enzyme shows a half-life of 15 and 5 min, respectively. Isoprenoid biosynthesis; isopentenyl diphosphate biosynthesis via mevalonate pathway; isopentenyl diphosphate from (R)-mevalonate: step 1/3. Homodimer. Belongs to the GHMP kinase family. Mevalonate kinase subfamily.