Can anyone tell me any possible dangers/risks that could happen if a wire overheats even if it's insulated properly?
Answers to your previous posts related to this subject have pointed out that the primary function of electrical insulation is not to prevent electrical overheating. Assuming you now understand that, I will attempt to answer your current question.
The possible risks are overheating causing thermal degradation of insulation leading to failure of insulation to protect against electric shock, short circuits and ground faults.
The primary concern is for electrical insulation being the “victim” of overheating. Overheating can degrade the electrical insulating properties of insulation so that the insulation no longer provides protection against electric shock. If the insulation is between live conductors or between live conductors and ground, its failure could also increase the risk of short circuits and ground faults increasing the risk of fire and shock. Of course if the overheating is high enough it could directly ignite the insulation.
In order to reduce these risks in the case of general use wiring, the principal safeguard is to reduce the likelihood of overheating. This mainly involves using properly sized conductors for the intended currents and coordinating that with properly sized overcurrent protection (fuses and circuit breakers).
Insulation can also be subjected to thermal degradation due to exposure to high temperatures in its environment, such as contact with high temperature external surfaces. If the temperatures are known insulation with an adequate temperature rating should be used.
This only touches on the subject. But I hope it gives you a better understanding.
When electric wires overheat, there are several dangers. As was said, if the temperature is high enough, the rubber insulator may melt away. The melted rubber, if it alights on a flammable substance, may cause fires. But also, the now exposed wire wilol not only be an electrocution danger, it causes current to bleed out to the sorroundings. This lessens the power feeding the equipment as a side effect. Although this was already said. And also, we know that the resistance of a metal depends on its temperature. As temperature increases, resistance decreases. As resistance decreases, current increases. According to Ohms law. In the case that there are electrical appliances or components attached across the wire, the current may go over the set limit and blow the equipment.