Overheating is definitely a cause for concern here. NEC Table 310.15(B)(2)(a) shows derating of conductors when there is more than 3 in a raceway. A 12 awg. copper THHN insulation copper conductor is good for 25 amps with not more than 3 wires in the raceway. When a raceway exceeds 20 wires it needs to be derated to 45% of 25, or 11.25 amps. Taking it one step farther if the number of conductors exceed 40, it derates to 35% or 8.75 amps. All of this derating is to allow for cooling of the conductors. I’d take a real close look at the whole electrical system. When I was wiring houses we were told if nothing else, make the panel look good, most inspectors will stop looking further if it looks good.
Attached is the panel in my house I did 17 yrs. ago