Looking at the details provided in the question, your objective is to create a heating system that is non polluting and requires no external energy source. The temperature of the room being heated has to be kept between 30 C and 40 C. You intend to accomplish this by using a gas and varying the pressure by less than 50 psi or 344738 Pa.
It is not possible to heat a room without the use of an external energy source. If the temperature of the room is less than the external temperature, heat flows in from outside till thermal equilibrium is reached. On the other hand, if the external temperature is lower than that in the room, heat flows out.
Now let us see what happens to a gas as the pressure applied is changed. The ideal gas equation gives the relation P*V = n*R*T where P is the pressure, V is the volume, n is the number of moles of the gas, R is the gas constant and T is the temperature. Temperature is directly proportional to the pressure, if the other factors are kept constant. So the gas can be heated by compressing it and cooled by allowing it to expand. In a room heating system, the gas can be compressed in a container kept inside the room, this would raise the temperature and if the container is made of a thermally conductive material, heat would flow into the room. The gas is then moved outside the room and allowed to expand. As this cools down the gas, it absorbs heat.
This may seem like a method of heating a room without using any energy, but the change in pressure of the gas requires energy. It is not possible to heat a room, and maintain a particular temperature range, irrespective of what the external temperature is, without using external energy in some form.
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