Momentum loss due to friction in a system Consider two physically isolated objects. Object $A$ approaches $B$ with some initial velocity $v$ and slides over $B$ and due to friction both objects become relatively hot (compared to their initial temperature). This heat is then lost to the colder environment.
Can such a system of these two objects lose significant amount of momentum and energy in this way? Say 1% of their combined initial momentum?
 A: From the law of conservation of momentum, the momentum of an isolated system is a constant. A system is considered isolated if there is no net external force acting on the system. Then the vector sum of the momenta $mv$ of all the objects of a system cannot be changed by interactions within the system.
Consider your objects A and B as being two blocks of equal mass which together constitute a system (See the figures below). Let B be initially at rest on a frictionless surface. Block A has an initial horizontal velocity of $V_i$ with respect to block B just prior to contacting and sliding upon block B where there is kinetic friction between them. Block B does friction work on block A bringing it to rest on block B. Block A exerts an equal an opposite force on block B (Newton's 3rd law) causing it to accelerate forward (as it is the net external force on B).
The final condition (FIG 2) has both blocks moving together with a final velocity $V_f$. The situation is analogous to a completely inelastic collision between two objects, except that friction for the inelastic collision is internal friction instead of surface friction.
Ignoring air resistance, the only external forces acting on the two block system are the downward force of gravity and the equal and opposite normal force acting upward on block B, for a net vertical force of zero. Given that the friction force between the blocks is an interaction within the system, the two block system is an isolated system and therefore momentum of the two block system must be conserved.
The initial momentum of the system is that of block A, which is $mV_i$. The final momentum of the system is that of the two blocks moving together of $mV_{f}+mV_{f}=2mV_f$. For conservation of momentum,
$$mV_{i}=2mV_f$$ thus
$$V_{f}=\frac{1}{2}V_i$$
The initial kinetic energy of the system is
$$KE_{i}=\frac{1}{2}mV_{i}^2$$
The final kinetic energy of the system is
$$KE_{f}=\frac{1}{2}(2m)V_{f}^{2}=mV_{f}^{2}=m\biggl (\frac{V_{i}}{2}\biggr)^2=\frac{1}{4}mV_{i}^2$$
For a loss of kinetic energy of $\frac{1}{4}mV_{i}^2$ which is eventually dissipated as heat.
As a final point, if A alone is considered to be the system then the friction force exerted on it by B would be an external force on the system, and the momentum of A alone will not be conserved (it decreases). The same would apply to B if B alone is the system as its momentum will increase.
Hope this helps.

