The right thing is to write high or, better, in the singular, height meaning time culmen, main, high or critical of an event, a time or period. This meaning is the most used since more than one century ago by the speakers, even if originally it meant the opposite: very cold, icy. Said someone, in febrile or comatose state, it was very cold, in which case the doctors said that it reached its hot as almost cadaverous cold time. Today anyone repair this antithetical meaning change.