There was a small box in the control room that recorded temperatures. What was that for?

That was a bathythermograph. As it appears, it recorded water temperatures at various depths. Submarines changed depths regularly just to see what the temperatures were. They were looking for abrupt changes in the temperature of the water.

Those abrupt changes are called thermoclines or layers. Changes in temperature also meant changes in density and that distorted sonar. If the temperature difference was large enough, sonar was reflected and a submarine could hide below the layer. In either case, anyone above who was searching for the boat probably had an inaccurate picture of where it was.

However, if sound was being distorted or reflected by a layer, the crew may not have had an accurate picture of what was above them. Caution was advised.

The bathythermograph (BT) was first developed in 1934 by Woods Hole Oceanographic Institute. It was first tested for submarine use in 1942. It could locate a “shadow zone” for a submarine to hide in.

(“USS Pampanito, Killer-Angel”, by Gregory Michno, page 66.)