Hi mattbrid and welcome to the forum.
In general, all solid-state amplifiers operating into a 4-ohm load will pass more current through the output transistors (because the resistance is less, 4 ohms as opposed to 8 ohms), so the output section will always run hotter than with an average 8-ohm system. Also, if you measure amplifier distortion with a 4-ohm load, it will always measure higher, but it will still be far below audibility unless the amp approaches clipping or clips.
All AV receivers contain some form of protection circuitry; most have thermal monitors on the output stage so if it gets too hot, the receiver will shut down before the output devices get damaged. There is usually a current-flow monitor as well, so if current flow becomes excessive, the protection circuit will either shut down the receiver or greatly reduce power output (current flow) to protect the output stage. Onkyo receivers a decade ago had overly touchy protection circuitry that would shut them down with 4-ohm loads and I would never recommend them for driving the Axiom M80s. Recent Onkyo models are much better, but since your owner's manual doesn't specify what the amp's power output is into 4 ohms, I suspect that there would be some type of current-limiting that kicks in to reduce power output into 4-ohm loads.
As other posts have noted, be careful about high-volume playback with 4-ohm speaker loads and if you hear any distortion or harsh, edgy quality in the sound, immediately turn down the volume.
Regards,
Alan
