In the case of the prior mindstream, its destiny is determined by its karmic perceptions and inclinations. When it enters a new body, it will not have consciousness of its previous body, will not be aware of it or its transformations, will not feel the cold of the preservation tank. When its prior body revives, it will not feel the revival, the return of heat, and the animation of its form by a new mindstream. Like someone who has abandoned a house that becomes occupied by a new person, it will have no knowledge of that persons presence, what they are doing in the rooms, or how they are treating the house.
Nevertheless the new mindstream and old mindstream in the revived body have much in common. They share the karmic propensities that cause the mind to incarnate into a body of that type, with those specific qualities and capacities. It will also share the karmic propensities that cause it to have certain experiences, attachments, preferences and so forth. However because the body is revive in the future, the more time passes the more its karma that determines its place of living will be different from the original inhabitant. This is because if you were frozen today and the body was revived in a hundred years, society will have changed much, all the external conditions will be different, quality of life, and so forth. In the same way similar houses attract similar types of people. Some people want yards, balconies, decks, tall ceilings, simplicity or elegance. So a simple abode is simple in the 50's and simple today, although external conditions have changed, still in both cases people who appreciate simplicity end up in the same kind of abode.
If you think "When the body is revived, the old person returns to it" you are making the fundamental error in thinking that the mind is ever in ownership of a thing called a body, that the mind is somehow inherently connected to the body, and that the mind is somehow inherently part of the body. Its the error in thinking that the body is anything more than Rupakaya manifesting inseparable from Dharmakaya. If it was the case that the mind was inherently a part of the body, then upon death your mind would experience all the transformations of the physical form, down to the very dispersal of all its elements into atomic particles. The mind would be endlessly divided into numerous consciousnesses until one was conscious of having as many bodies equal to the number of atoms in ones body today.
However we know this is not the case. The body is merely a conditioned thing, a set of conditions that we incarnate into based upon our karma. When a new mind enters the body, it will do so as a result of its karma. When the old mind enters a new body after the bardo, it will also do so based on conditions. The two minds share commonalities in karmic propensities, and they also share the same essential Buddha nature. Furthermore they will share similar experiences because the old body contains memories and impressions stored in the brains neural network. This will form the framework that the new mind will enter into, and although it may appear to be the same person because they will have memories of the same people, places and things, there was never any person in the first place and all that ever existed was ones own deluded and conditioned perceptions of having a body, a self, and so forth.
If the body was part of the mind, not only would it undergo all of its transformations after death, but reincarnation would be impossible since it would not be possible for the mind to separate itself from the body. Instead, what is impossible is to separate minds perceptions of the body from its own essential nature. When this is recognized, one acts with enlightenment towards bodily perceptions, and when it is not one acts with delusion.