Suppose I have $N$ fermions in an 1D infinite potential well. At $T=0K$, the fermions will occupy the lowest $N$ states and the wave function looks like:
$$|\phi_0\rangle= \frac{1}{\sqrt{N!}}\begin{vmatrix} \psi_1^1 & \psi_2^1 & \psi_3^1 & \cdots & \psi_N^1 \\ \psi_1^2 & \psi_2^2 & \psi_3^2 & \cdots & \psi_N^2 \\ \psi_1^3 & \psi_2^3 & \psi_3^3 & \cdots & \psi_N^3 \\ \cdots & \cdots & \cdots & \cdots & \cdots \\ \psi_1^N & \psi_2^N & \psi_3^N & \cdots & \psi_N^N \\\end{vmatrix} $$
Now if I increase the temperature, there will be some occupation at $|\psi_{N+1}\rangle$ and some $|\psi_A\rangle$ will be empty. However, for particle in 1D box, we know that the wave functions are orthogonal, i.e. $$\langle\psi_A|\psi_{N+1}\rangle=0$$
Then what is it which is responsible for the transition of a fermion from $|\psi_A\rangle$ to $|\psi_{N+1}\rangle$?