Relative Humidity is essentially the percentage of water held in air expressed as a percentage of the maximum amount the air can hold.
Air can hold more or less absolute amount of water depending on temperature and pressure
When you pressurize the air ( blow it through a CPAP at say 9 cm H2O - a simple measure of pressure when small increments are used) it can hold more water. It doesn't decrease the amount of water in the air from the intake - it just increases the air's ability to hold water. This is experienced as a lower relative humidity - the percentage of the water in the air relative to the amount it could hold is decreased and we feel it as drier leading to all the effects we know from un-humidified air.
Similarly with temperature - if we heat air - it can absorb more moisture than cold air. If we cool it, it can hold less, This is why you get dew on the car on cold mornings. So if we simply heated the air without the water tank - it would feel even dryer, which is why the instructions for the humdifier tanks say to never run it without water. I seriously doubt at the temperatures we are talking about it can harm anything, but it will feel like the wind from the Sahara is going up your nose.
Heating a tank of water gives off water vapour into the pressurised air - the goal isn't really to heat the air but force vapour off the water into the air. Warmer air is a side effect, that leads to rain out if the air in the tube cools too much - balancing the vapour forced off the water tank is one way of controlling rain out, but only if doing so gets enough moisture into the air for your comfort - otherwise you need to heat the tube to maintain the air's ability to carry more water up, and then release it once it gets to your nose, assuming some cooling effect from the mask. mind you in winter (or the fridge my wife turns our bedroom into in summer), the warmer air is pleasant.
Conversely Cooling the air will make it feel wetter.
I will go dust off the old text books for the formula - but chilling the pressurized air could also increase its humidity to where it balanced the humidity reduction from increasing its pressure. The question is, how much colder would you need for each cm H2O to balance the pressure effect so the relative humidity remained unchanged from the air in the room. The thermodynamic equations are not trivial but an interesting problem
Really interesting idea -