For free expansion of an ideal gas, the external pressure is zero ($p_{ext} = 0$). Therefore, the work done is zero ($w = -p_{ext}\Delta V = 0$). Under adiabatic conditions, there is no heat exchange between the system and the surroundings, so $q = 0$. According to the first law of thermodynamics, $\Delta U = q + w = 0 + 0 = 0$. For an ideal gas, internal energy depends only on temperature. Since $\Delta U = 0$, the change in temperature is also zero ($\Delta T = 0$). Thus, the correct conditions are $q=0$, $\Delta T=0$, and $w=0$.