Collision KE converted to heat

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Suppose we have to balls with same mass and same speed shot against each other. Let's assume that the collision is completely inelastic. Then both balls will drop to the floor as all their kinetic energy is converted to heat by friction. However - heat is just another word for the speed of the particles the make up the balls. Thus they will receive a boost in velocity and thereby momentum.

Can the lost energy therefore, be interpreted as something that makes the momentum of the individual balls more disorganized?
 

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Momentum is a vector. After the collision the mean speed of random vibrational motion of the particles will be higher than before, but the mean momentum component in each of three orthogonal directions will be zero (neglecting the balls dropping).

Before the collision both balls did have momentum. But the two balls' momenta were equal and opposite, so total momentum is zero both before and after the collision.