For free expansion, external pressure $P_{ex} = 0$, so work $w = -P_{ex}\Delta V = 0$. For an adiabatic process, $q = 0$. By the first law of thermodynamics, $\Delta U = q + w = 0$. Since internal energy of an ideal gas depends only on temperature, $\Delta U = 0$ implies $\Delta T = 0$.