We determine from first-principles the Curie temperature Tc for bulk Co in the hcp, fcc, bcc, and tetragonalized bct phases, for FeCo alloys, and for bcc and bct Fe. For bcc-Co, Tc=1420 K is predicted. This would be the highest Curie temperature among the Co phases, suggesting that bcc-Co/MgO/bcc-Co tunnel junctions offer high magnetoresistance ratios even at room temperature. The Curie temperatures are calculated by mapping ab initio results to a Heisenberg model, which is solved by a Monte Carlo method.