The performance of precoded integer forcing equalization for communication over the compound multiple-input multiple-output channel is investigated. It is known that an integer-forcing receiver applied to streams precoded using the encoding matrix of a perfect linear dispersion space-time code achieves capacity up to a constant gap. Hence, it attains an arbitrarily large fraction of capacity for sufficiently large rates. It was recently shown that allowing for a small outage probability, the integer-forcing receiver achieves a large fraction of capacity when random unitary precoding is used over the spatial dimension only. This work demonstrates that further improvement can be achieved by extending the random unitary precoding to the temporal domain. Further, it is shown that at moderate transmission rates, such precoding outperforms perfect linear dispersion space-time precoding.