It seems there is some confusion between the cold and hot molding processes used historically in aircraft production. This probably stems from the use of common brand names instead of the full designation or at least the chemical family.
The Mosquito fuselage was not hot molded, it was cold molded. The initial glue was a casein one, then they switched to a UF glue. Both are classed as water resistant, not waterproof. UF glue will polimerize at room temperature but heat greatly accelerates the process, reducing clamping time. The Mosquito assembly lines used mainly electric strip heaters to accomplish this.
At the time the UF glue was only available in a two part form, the resin and a powdered hardener, today its also available as a dried powder mix wich is activated by mixing it with water. In this form it is known to modern woodworkers as plastic resin glue, produced for example by Weldwood.
During the same time frame there was another process already in use before UF glues were invented for producing aircraft laminated parts (wood and wood metal), involving a different glue family, the PF's. This is essentially a form of bakelite, and requires high temperature and pressure for curing. This was commonly done by using a steam autoclave, and this equipment was later used for the production of hot molded small boats. Small boats only because the autoclaves were sized for propellers and aircraft control surfaces, not fuselages. The glues from the PF family are classed as waterproof, and there were several types and formulations available. Google Tego film, Duramold and Redux for historic references. This is the glue you see today in all exterior/WBP plywood.
Also during WW2 another glue family was invented, the PRF's, aka resorcinol. This is a waterproof glue that requires high pressure but much lower temperatures (about half) then PF's for polymerization, and is classed as a cold molding glue. It was widely used in boatbuilding before epoxy became common and is still available today as a specialized woodworking glue, altough its use has declined to the point where small customers have to actually check the expiration date of the batch when they buy it, or preorder and wait.