Below what temperature does a semiconductor stop behaving intrinsically?

I understand that for an intrinsic semiconductor $n=p$ where $n$ is the electron carrier concentration and $p$ is the hole concentration. My question is how to calculate the temperature at which the semiconductor is no longer intrinsic?

The electron carrier concentration is given by,
$$n = N_c exp[frac{mu – E_g}{k_B T}]$$ where $E_g$ is the band gap energy, whilst
$$p=N_v exp[frac{-mu}{k_B T}]$$

We are also told that the intrinsic carrier concentration at $300K$ is $2 text{x} 10^{16} m^{-3}$
Assuming that the density of states $N_v ,N_c$ are constant, surely we can’t just equate these and solve for $T$, as they already presuppose the semiconductor is intrinsic?