About 10 minutes of your time...provided you're comfortable with removing the lid of the Axe-Fx.
I had the same issue with MK-I. After reading through some threads, I discovered it was most likely a loose ribbon cable. I recently re-wired my rack, so it was a perfect time to remove the Axe-Fx from the rack and fix the problem.
After you remove the screws on top, holding the lid in place, carefully lift it up...the fan is attached to the lid and the power cable is plugged into the main chassis. In my case, the connector popped off, but it only plugs in one way.
Carefully remove and re-seat the ribbon cable that's plugged into the LCD PCB, on the inside, front face of the unit. Plug the fan back in, if necessary, put the lid on, tighten the screws and that's it.
It's been about a week for mine and the problem appears to be fixed!