To answer your question, I think it would be helpful to first address what air pressure is and how you can have relatively localized changes in pressure.
In a nutshell, gas pressure is the force exerted on the environment or objects in the environment by the random collisions of gas particles as they float around. The speed and direction at which those particles move is related to the temperature of the gas and its flow; for example, air that's moving at high speed (like a gust of wind) exerts more pressure on a surface in the flow than still air would exert under the same conditions.
Pressure is related to volume, temperature, and gas species by the Ideal Gas Law: Pressure = (Amount of Gas * Temperature) / Volume. Basically, increase the temperature and hold volume and amount of gas constant, and the pressure will rise. Shrink the volume and hold temperature constant, and the pressure will rise.
But gasses are not uniform in composition, and their constituent particles can't move instantly. If you take a room full of air, the air on one side might be a bit cooler than the air on the other side. Air near the air conditioner might be moving, while air on the other side of the room might not. But the whole room is still filled with air and the particles are free to move around and interact with one another. So say you increase the temperature of a small pocket of air in the room. This would cause the particles in that pocket to move faster, and collide more often with their surroundings, thus increasing the pressure. But their neighbor particles will be moving at their original speed until something hits them, so the pressure outside of that suddenly warmer pocket would stay the same for a short time. This is the principle that gives rise to regions of varying pressure. But as the particles collide, they'll transfer their energy to their neighbors, and the little pocket of higher temperature, higher pressure air will dissipate across the room in a very short time.
This dissipation is the problem with your particular scenario. Within the realm of physics, it's doable if you raise the temperature very rapidly, but the pressure change won't stay local. As the warmer, higher-pressure air particles collide with their neighbors, the pressure increase will move outward in a wave, diminishing the further it spread, so your other camping group would feel a shockwave. And the amount of temperature change necessary to cause physical trauma to your campers would be immense: although you only need to increase the local pressure by around 10 pounds per square inch (almost double normal atmospheric pressure), your volume is on the order of 1,200 cubic feet! You'd have to raise the temperature by more than a factor of 10, instantaneously to get the desired effect.
So, as mentioned in other answers, magic is probably the only way to do what you're trying to accomplish without nasty side effects like shockwaves and plasmas.