In a closed system, when the temperature increases, the molecules within that system move more rapidly due to the added energy. This increase in kinetic energy means that the molecules collide with the walls of the container more frequently and with greater force. According to the principles outlined by the ideal gas law (PV = nRT), where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature, it becomes clear that with a constant volume and amount of gas, an increase in temperature must result in an increase in pressure.
This relationship is a fundamental concept in thermodynamics and can be observed in everyday scenarios, such as a sealed container of gas that expands when heated. Thus, in a closed system, higher temperatures translate to higher pressures, making the assertion that increasing temperature increases pressure in such conditions accurate.