Why does gas pressure increase with temperature?
Pressure and Temperature have a direct relationship as determined by Gay-Lussac Law
Pressure and temperature will both increase or decrease simultaneously as long as the volume is held constant.
Therefore if temperature were to double the pressure would likewise double. Increased temperature would increase the energy of the molecules and the number of collisions would therefore increase causing an increase in pressure. More collisions within the system, leads to more collisions with the surface of the container and therefore more pressure within the system.
Take a sample of gas at STP 1 atm and 273 K and double the temperature.
P = 2 atm
Doubling the temperature, likewise doubled the pressure.
I hope this was helpful.