  Planetesimals in the primordial disc may have experienced a collisional
cascade. If so, the comet nuclei later placed in the Kuiper belt, scattered
disc, and Oort Cloud would primarily be fragments and collisional rubble piles
from that cascade. However, the heating associated with the collisions cannot
have been strong enough to remove the hypervolatiles that are trapped within
more durable ices, because comet nuclei are rich in hypervolatiles. This places
constraints on the diameter of the largest bodies allowed to participate in
collisional cascades, and limits the primordial disc lifetime or population
size. In this paper, the thermophysical code NIMBUS is used to study the
thermal evolution of planetesimals before, during, and after catastrophic
collisions. The loss of CO during segregation of $\mathrm{CO_2:CO}$ mixtures
and during crystallisation of amorphous $\mathrm{H_2O}$ is calculated, as well
as mobilisation and internal relocation of $\mathrm{CO_2}$. If an amorphous
$\mathrm{H_2O}$ host existed, and was protected by a $\mathrm{CO_2:CO}$ heat
sink, only diameter $D<20\,\mathrm{km}$ (inner disc) and $D<64\,\mathrm{km}$
(outer disc) bodies could have been involved in a collisional cascade. If
$\mathrm{CO_2}$ was the only CO host, the critical diameters drop to
$D<20$-$32\mathrm{km}$. Avoiding disruption of larger bodies requires a
primordial disc lifetime of $<9\,\mathrm{Myr}$ at $15\,\mathrm{au}$ and
$<50$-$70\,\mathrm{Myr}$ at $30\,\mathrm{au}$. Alternatively, if a
$450\,\mathrm{Myr}$ disc lifetime is required to associate the primordial disc
disruption with the Late Heavy Bombardment, the disc population size must have
been 6-60 times below current estimates.
