Could you please describe the Temptation scene in The Murder in the Cathedral as a reflection of Becket's "id"?
The crucial point in this sequence in the play is, I think, the appearance of the Fourth Tempter.
The Freudian id represents the hidden, unconscious desires of the individual which are often repressed because they are in conflict with the laws and prohibitions (especially about physical and sexual pleasure) of human society. With regard to Beckett's tempters, we can only take the analogy between them and the id so far. It is true that the expected, first three, Tempters are more conventional representations of this concept. But the very first statements of the Fourth Tempter seem eerily to correspond in a more subtle or deeper way to the repressed subconscious:
As you do not know me, I do not need a name,
And, as you know me, that is why I came.
You know me, but have never seen my face.....
As I understand the Tempter's counsel, it is that Beckett fulfill a mission to become a martyr by being defeated by the King, and thereby gain the eternal glory of being worshipped by posterity for all time. In this, Beckett will have defeated the King in death, and for eternity.
There is a paradox inherent in this. Normally we would think that the purely spiritual glory sought by Beckett, and recommended to him by this Tempter, would be the reverse of the desires of the subconscious, which we see as seeking a physical (or specifically sexual) fulfillment, and eventually a transgression of society's rules. So the Fourth Tempter's advice is not temptation at all, but a fulfillment of Beckett's divine mission of self-denial. Yet the paradox is that by seeking this eternal glory Beckett, it is implied, is simply trying to acquire another form of power. Eliot seems to be asking if this--power in any form--is the deepest desire of the unconscious, and it appears in an even more naked form as an eternal force that will result in Beckett's being worshipped for all time. By contrast Henry II, or any king, will just have a handful of years in power.