37 Celcius is the average human body temperature so your point presumably is that a person should not gain or lose heat energy in either situation.  However human beings, as warm-blooded animals, produce heat internally and need to get rid of an excess.  The normal way in air is by evaporation of sweat (there are limits on how well this works depending on humidity, hydration of the body involved, air movement etc.)  which requires high blood flow to the skin.  This, and the build-up of salt and oils from the sweat, will make the person feel grubby and uncomfortable.  In water any sweat will be washed away but the better conduction/convection of heat in water should remove excess heat fairly rapidly.  Despite this I wouldn't advise long-term immersion - damage to skin will occur within a few hours.