From the question I assume you are new to Buddhism so will answer accordingly.
There is no scientific explanation for feeling pain let alone not feeling it. However, there are explanations. Indeed, the whole of Buddhist doctrine might be seen as an explanation of how to transcend suffering. You would need to study the 'Four Noble Truths'.
A very famous case is the horrific crucifixion and torture of the Sufi sage Al Hallaj. It seemed not to bother him and he expresses disappointment when one of his students sheds tears for him, for it gives away his lack of understanding that there is nobody there to suffer.
The explanation would be the ability of human beings to discover that the self that suffers is not real and to stand apart from their thoughts, feelings, sensations and emotions. We can all do this to some extent and find ourselves forced to do it situations of great pain. Many people come to Buddhist practice and that of other traditions by way of lengthy painful experiences. They discover that the pain may be viewed objectively without any sense of ownership such that they can say 'There is pain', and not 'I am in pain'.
A full explanation would require delving into the nature of consciousness and personhood and this would take us beyond 'scientific consciousness studies' and academic philosophy, while an understanding of the explanation would require a lot of practice and personal research.
This ability to transcend suffering is in the nature of consciousness. The comment by Aurobindo below indicates that it is a recognition that only our 'surface being' suffers, and this allows practitioners to display great feats of suffering. But it cannot be a theory. It has to be a reality for us or it is not the case for us. Thus practice is required for such feats, not book-learning.
"One might almost say that our surface being is only the deeper eternal self in us throwing itself out as the adventurer in Time, a gambler and speculator in infinite possibilities, limiting itself to the succession of moments so that it may have all the surprise and delight of the adventure, keeping back its self-knowledge and complete self-being so that it may win again what it seems to have lost, reconquering all itself through the chequered joy and pain of an aeonic passion and seeking and adventure." (Sri Aurobindo, The Life Divine)
Thus to overcome suffering would mean realising that our surface being is a construction, much as Dennett describes it, and not our true being. For a truly realised being there would be no suffering and no person to suffer, and this is the meaning of the Four Noble Truths.
On a personal note, aged seventeen I suffered a lot of intense pain for a period due to an operation that went wrong. I had no choice but to distance myself from it and found that this is possible. It was only four decades later that I discovered Buddhism and found an explanation. There is more to human being (or perhaps less) than the natural sciences are able to discover. Hence the placebo effect may be effective in reducing pain. For a full reduction the Buddha's medicine would have to be ingested. A truly skilled monk may self-immolate without the slightest worry about pain and death. They are past all that nonsense.
Whether we believe this is not important since believing it isn't going to help. But even if we know nothing about Buddhist teachings the next time we're in great pain it may be a good chance to perform some experiments. In practice it is said that we discover not simply that we do not suffer but that there is nobody to suffer. Regrettably this knowledge is not easily won, but even a little familiarity with the skills required will help us when we are in pain.
The natural science may be able to verify that the behaviour of some people indicates an ability to transcend pain but is not able to study consciousness so cannot provide an explanation. The science of Yoga, however, as described by Patanjali, or Buddhist practice allows us to know the explanation and make it our reality.
Aurobindo (ibid) also says this.
"In our ordinary life this truth is hidden from us or only dimly glimpsed at times or imperfectly held and conceived. But if we learn to live within, we infallibly awaken to this presence within us which is our more real self, a presence profound, calm, joyous and puissant of which the world is not the master - a presence which, if it is not the Lord Himself, is the radiation of the Lord within. We are aware of it within supporting and helping the apparent and superficial self and smiling at its pleasures and pains as at the error and passion of a little child."
You may find some interesting youtube videos on this topic but I don't know of any on this exact topic. Any decent book on meditation ought to cover the main points and explain the abilities of these self-immolating monks.
Here are some suttas about giving up pleasure and pain.