Fireproof

20 And he ordered some of the mighty men of his army to bind Shadrach, Meshach, and Abednego, and to cast them into the burning fiery furnace. 21 Then these men were bound in their cloaks, their tunics,[e] their hats, and their other garments, and they were thrown into the burning fiery furnace. 22 Because the king's order was urgent and the furnace overheated, the flame of the fire killed those men who took up Shadrach, Meshach, and Abednego. 23 And these three men, Shadrach, Meshach, and Abednego, fell bound into the burning fiery furnace.

24 Then King Nebuchadnezzar was astonished and rose up in haste. He declared to his counselors, “Did we not cast three men bound into the fire?” They answered and said to the king, “True, O king.” 25 He answered and said, “But I see four men unbound, walking in the midst of the fire, and they are not hurt; and the appearance of the fourth is like a son of the gods.”

26 Then Nebuchadnezzar came near to the door of the burning fiery furnace; he declared, “Shadrach, Meshach, and Abednego, servants of the Most High God, come out, and come here!” Then Shadrach, Meshach, and Abednego came out from the fire. 27 And the satraps, the prefects, the governors, and the king's counselors gathered together and saw that the fire had not had any power over the bodies of those men. The hair of their heads was not singed, their cloaks were not harmed, and no smell of fire had come upon them (Dan 3:20-27).

There are readers who find this unbelievable or hard to believe. In that regard, the description of Polycarp as fireproof presents a striking parallel to Daniel's friends in the furnace:

Polycarp 15:2

The fire, making the appearance of a vault, like the sail of a vessel filled by the wind, made a wall round about the body of the martyr; and it was there in the midst, not like flesh burning, but like [a loaf in the oven or like] gold and silver refined in a furnace. For we perceived such a fragrant smell, as if it were the wafted odor of frankincense or some other precious spice.

Polycarp 16:1

So at length the lawless men, seeing that his body could not be consumed by the fire, ordered an executioner to go up to him and stab him with a dagger. And when he had done this, there came forth [a dove and] a quantity of blood, so that it extinguished the fire; and all the multitude marvelled that there should be so great a difference between the unbelievers and the elect.

http://www.earlychristianwritings.com/text/martyrdompolycarp-lightfoot.html

The martyrdom of Polycarp is presented as an eyewitness account. To my knowledge, it's generally considered to be authentic. 

The account includes a premonition (5:2), and audible divine voice (9:1). Although an unbeliever will dismiss that as legendary embellishment, it helps to explain Polycarp's indomitable courage in the face to death by torture.