This is very similar to this question:
However, I feel as though an important caveat was not resolved for me which is why I am asking it here.
We have that in a collision (namely, an inelastic one) energy is not necessarily conserved among the objects in the collision. A common explanation that makes sense to me is that the energy of the collision is converted into heat/sound energy in the outlying particles. However, if these outlying particles that were once stationary or moving more slowly begin to move more quickly (due to an increase in kinetic energy), wouldn't their momentum increase as well due to an increase in velocity?
One explanation I have for this is because particles will vibrate in such a way that the net velocity remains unchanged (i.e. there will be equal acceleration in all directions among the particles that heat up). However, I have no conclusive reason to believe that this is the case.