  The binary Monte Carlo (MC) collision algorithm is a standard and robust
method to include binary Coulomb collision effects in particle-in-cell (PIC)
simulations of plasmas. Here, we show that the coupling between PIC and MC
algorithms can give rise to (nonphysical) numerical heating of the system, that
significantly exceeds that observed when these algorithms operate
independently. We argue that this deleterious effect results from an
inconsistency between the particle motion associated with MC-collisions and the
work performed by the collective electromagnetic field on the PIC grid. This
inconsistency manifests as the (artificial) stochastic production of
electromagnetic energy, which ultimately heats the plasma particles. The
MC-induced numerical heating can significantly impact the evolution of the
simulated system for long simulation times ($\gtrsim 10^3$ collision periods,
for typical numerical parameters). We describe the source of the MC-induced
numerical heating analytically and discuss strategies to minimize it.
