In an adiabatic process, there is no exchange of heat between the system and the surroundings, so $q = 0$. According to the first law of thermodynamics, $\Delta E = q + w$. Therefore, $\Delta E = w$. When a system expands, work is done by the system, making $w$ negative. Consequently, the internal energy ($\Delta E$) of the system decreases, which also leads to a decrease in temperature.