5.56 ammo is generally not "HOTTER" than .223. In fact, some commercial .223 cases have a larger powder capacity than do 5.56 cases. The difference in the chambering of the two cartridges is that most .223 chambers have a shorter leade (throat area) and headspace. This can lead to increased pressure if a 5.56 cartridge is fired in the rifle chambered for .223. The 5.56 chambers are more generous and allow 5.56 cartridges to operate at a lower pressure. Additionally, .223 conforms to SAMMI specs whereas the 5.56 does not (regrading pressure limits).
While many people think nothing of interchanging the two rounds, it is not advisable to shoot 5.56 in rifles designed for .223 - most all manufacturers warn of this in the manuals that accompany their rifles.
Blessings.
Paul