Also, if the water temperature had been 14 degrees below zero, the ship wouldn't have sunk because the sea would have been frozen.
The ship might not have been sunk had the skipper not turned on his navigation lights, a foolish thing to do in a war zone.
Heinz Schön, who carried out extensive research into the sinking during the 1980s and 1990s, concluded that the Wilhelm Gustloff was carrying a crew of 173 (naval armed forces auxiliaries), 918 officers, NCOs, and men of the 2 Unterseeboot-Lehrdivision, 373 female naval auxiliary helpers, 162 wounded soldiers, and 8,956 civilians, among them an estimated 4,000 children, for a total of 10,582 passengers and crew.
Per wikipedia
The ship left Gotenhafen early on 30 January 1945, accompanied by the passenger liner Hansa, also filled with civilians and military personnel, and two torpedo boats. The Hansa and one torpedo boat developed mechanical problems and could not continue, leaving the Wilhelm Gustloff with one torpedo boat escort, the Löwe. The ship had four captains (three civilian and one military) on board, and they could not agree on the best course of action to guard against submarine attacks. Against the advice of the military commander, Lieutenant Commander Wilhelm Zahn (a submariner who argued for a course in shallow waters close to shore and without lights), the senior civilian captain—Friedrich Petersen—decided to head for deep water. When he was informed by a mysterious radio message of an oncoming German minesweeper convoy, he decided to activate his ship’s red and green navigation lights so as to avoid a collision in the dark, making the Wilhelm Gustloff easy to spot in the night. The source or authenticity of this radio message was never confirmed and there was no oncoming German minesweeper convoy as it later turned out.
Because the Wilhelm Gustloff had been fitted with anti-aircraft guns it was not marked as a hospital ship (unlike the Soviet hospital ship Armenia incident in 1941), no notification of it operating in a hospital capacity had been given and, as it was transporting combat troops, it did not have any protection as a hospital ship under international accords
Per Wikipedia.