"The first rule of being interrogated is that you are the only irreplaceable person in the torture chamber. The room is yours, so work it. If they're going to threaten you with death, show them who's boss. Die faster."
IN THIS ONE... The Doctor is trapped in a puzzle box designed to terrify and interrogate him.
REVIEW: There is no other episode of Doctor Who like this. Except for one small scene in which Clara figures as a memory/ghost, the Doctor is the only character to have lines in the story. He ends up talking to himself a lot - which he's noted before is a problem when he's without a companion - sometimes in his "mind palace", an idea ported from the Moff's own Sherlock, but well used (and it explains all those sequences where the Doctor broke the fourth wall this season, we were simply inside his mind). We'll discover that, in fact, the way a mere seconds become all the time in the world inside his mind, is what's happening on the macro scale, and the Purgatorial puzzle offered by this castle in the middle of a vast ocean is just an extension of the same investigation/interrogation/escape attempt, lasting forever on a limited loop. In both cases, we are inside his mind (though see Theories for a more complete answer), and should take the clue about the special door "I am in 12" as a hint, never mind all his most visceral fears being in there with him, and the frankly silly idea that you could punch a diamond wall down with time (which works if these are all mind constructs).
The second time we watch it, knowing what's really going on, we'll find plenty of foreshadowing and additional clues, like the Doctor saying "I will never stop" or that's he been in there "forever". Meditating on death and the afterlife, alone on stage, he's a Hamlet figure, but Yorick's skull is his own. The Doctor has two problems to solve: The puzzle and how to get out of it, and his deep grief over Clara's death. Because this bit of his life keeps repeating, he's not given much of a chance to fix the latter, so don't expect a big change once he's out, but this grief acts as a distraction to the former. The eerie figure of Clara standing with his back to him in his imagination and the despair he feels are impediments, but he manages to turn her memory into an advantage, a "teacher" figure who focuses his problem-solving abilities by writing the right questions on a black board. The Time Lords, meanwhile, have a single reason for putting him in there: Questioning him about the hybrid, which they believe he knows something about. The shocker ending where he claims to BE the hybrid is mere bluster, surely, and we're led to believe he's prepared to destroy his own people again if need be. They haven't become a peaceful society again, and everything screams Time War between their underhanded practices and the child in the desert the Doctor finds outside the Capitol, clearly meant to evoke young Davros at the start of the season.
Heaven Sent is a daring experiment that plays well to an older audience, but may be tougher on the kids. Not just because it takes its time, has many silent scenes, and can be obtuse on first and even second viewing, but because the Doctor dies on screen again and again, until his skulls form a reef around the castle. The number of cycles through the machine is impossible to calculate, as we don't know how many days are in each loop, but if the whole experience lasts billions of years, and each loop occurs several times a year, possibly dozens of times a year... Well, if the Doctor were to remember it all, it would be character-breaking. As it is, the simple knowledge that he's been trapped in that experience for all that time is enough to anger him, but how much of himself has he "purged"? This is perhaps a zero-sum game as far as character development goes, but we do get insights into the Doctor's psyche along the way, especially how he views his constant companion, death.
THEORIES: So the Doctor was inside his confession dial all along, but what ARE those things? Well, to grasp at an answer, we have to remember the Matrix. In Classic Who, this has been referred to as a telepathic hub where every Time Lord's knowledge (and consciousness?) goes after death, as well as a databank apparently connected to the TARDIS' telepathic circuits, making a record of every Time Lord's experience. We've also see people enter it physically through a portal, and some Time Lords seem adept at manipulating its inner landscape, drawing others into surreal nightmares (The Deadly Assassin, The Ultimate Foe). So it's the Time Lord internet, with an extra-dimensional component to it. The confession dial seems to me an adaptation of that technology. In the old days, Time Lords mostly stayed at home and didn't interfere with history, so you'd have ready access to the Matrix before (and during, since they die so slowly, shown here) they had to upload their knowledge to the hub. The Time War would have changed all that, and perhaps confession dials are the field version of the Matrix, a portable "drive" designed to debrief you after death. But since war corrupts technology to its own ends, perhaps they started using the dials for interrogation purposes; the Time Lords clearly have the means to turn the dial experience into a nightmare scenario designed to get the information out of someone. Normally, it should probably be a pleasant experience - and Missy's Nethesphere's is another example - until the dial is found and its info uploaded to the Matrix proper. Time Lord afterlife. Entering physically is possible just like entering the Matrix physically is possible (though one wonders why the Time Lords left the dial out in the desert), though probably not for "dying" personnel, who would just come out dying or dead anyway. (Some of this is confirmed in the next episode.)
REWATCHABILITY: High - It doesn't give answers up easily, but that's what makes this puzzle episode worthy of repeat viewings.