Suppose you have a piston of ideal gas that's thermally isolated from its surroundings. You compress the gas by pushing down on the piston. Question: Does the temperature of the gas change, and why? My answer: YES, it changes. Since [itex]\Delta U = Q + W[/itex], and work was done ON the gas (by compressing it), [itex]\Delta U > 0[/itex]. Since the energy of an ideal gas is only dependent on the temperature of the gas, this implies [itex]\Delta T > 0[/itex].