Here's how a recent author saw him, based on his autobiography and other sources.
"Carpathia’s greatest asset was her master. Captain Arthur Henry Rostron was known in his line as ‘the electric spark’ for his boundless capacity to get things done. Like all Cunard masters, he began his career in sail and his experiences in the wild seas off Cape Horn had given him a healthy respect for the ocean and its perils. On one terrifying occasion, his ship, Cedric the Saxon, was pooped by a gigantic comber that swept away her wheel, leaving the vessel broached to, with her sails in rags. That day he, ‘...saw fear in the eyes of men and found it no pretty sight.’ He had risen to command via a posting as chief officer on Lusitania during her sea trials. As a master, he had the happy knack of securing an efficient ship without antagonising his crew, though capable of tough methods when called for. As first mate of the barque Camphill, he had knocked seven bells out of an insolent seaman in the best Bully Forbes manner. He was not a typical master in appearance. Tall and lean, with piercing blue eyes, he lacked the air of the old sea-dog that made Captain Smith a favourite. Though of humble origins, he spoke in the measured and polished tones of an aristocrat. He had a firm religious belief in a ‘Higher Command’, who expected him to do his best without fear, and in times of crisis he visibly prayed for guidance. His life was devoted to the sea for forty-six years. In sail or steam, in peace or in war, his enthusiasm never flagged. James Bisset called him, ‘...one of the greatest merchant sea-captains of his time."
Rostron had a reputation for being rather cold and distant when meeting passengers. However, in the privacy of his quarters he sometimes displayed his more congenial side.
Personally, I suspect Rostron had a rather too good an opinion of himself. Certain events make me wonder if he was quite as efficient as he liked to think.
I had thought him rather a cold and aloof character (if admirable!), until I heard the anecdote about how he adored lighting bonfires, and the sheer delight he took in them. It made him seem more warm (no pun intended) and lively as a personality.