X-ray synchrotron experiments with in situ laser heating of iron in a diamond-anvil cell show that the high-pressure epsilon phase, a hexagonal close-packed (hcp) structure, transforms to another phase (possibly a polytype double-layer hcp) at a pressure of about 38 gigapascals and at temperatures between 1200 and 1500 kelvin. This information has implications for the phase relations of iron in Earth's core.