Step 1: Recall the method of cryopreservation.
Long-term preservation of animal cell lines is achieved by cryopreservation in liquid nitrogen.
Step 2: Identify the storage temperature.
Liquid nitrogen has a temperature of
\[
\boxed{-196^\circ\mathrm{C}.}
\]
At this temperature, cellular metabolism is effectively halted, allowing long-term storage.
Therefore,
\[
\boxed{(D)}
\]
is the correct answer.