I just replaced a Moen 1225 cartridge in a shower/tub combo. After completing the job, I turned the water back on and noticed there was only lukewarm water on the hot side. All the other faucets in the house dispense appropriately hot water. This is a rarely used shower/tub but had no previous problems with the water temperature. There was a coupling nut that fell out of the wall while removing the old cartridge; I have no idea the source of this and don't know if this is related to the problem. I don't notice a significant change in the water pressure from the hot to cold side. Would appreciate any assistance. (I am NOT plumbing savvy but have changed cartridges in the past with no problems.)

There was a coupling nut that fell out of the wall
That had to be just trash in the wall. No way you could be missing nut and not have a leak. Was probably something the plumber put between the pipe and the wall to keep the pipe in a certain position while he soldered. Or something that just fell inside the wall.

Is this a pressure balancing valve? Does it have something that looks like a big round plug on the cold side?

First suggestion would be to remove the cartridge and the turn on the water for about 10 to 15 seconds in case something is obstructing the hot side.

If that doesn't work then you will need to remove and flush the pressure balancing valve.

I agree, debris must have broken loose and is plugging the hot inlet. Shut off the main, remove the cartridge,hold a towel tightly over the opening of the valve body and have a helper turn on the water for a few seconds with you holding the towel to redirect the flow. Inspect and blow out the debris and reinstall, do not forget the clip. BTW why did you need to replace the cartridge?

Either trash or you can adjust the scald guard dial.