  The thermal expansion at constant pressure of solid CD$_4$ III is calculated
for the low temperature region where only the rotational tunneling modes are
essential and the effect of phonons and librons can be neglected. It is found
that in mK region there is a giant peak of the negative thermal expansion. The
height of this peak is comparable or even exceeds the thermal expansion of
solid N$_2$, CO, O$_2$ or CH$_4$ in their triple points. It is shown that like
in the case of light methane, the effect of pressure is quite unusual: as
evidenced from the pressure dependence of the thermodynamic Gr\"{u}neisen
parameter (which is negative and large in the absolute value), solid CD$_4$
becomes increasingly quantum with rising pressure.
