Interesting; our idea of consciousness however, is more like a stream, should this stream stop or get cut-off i.e. through heat death, the conscious simply halts its experience and well.. dies; if it were to keep making AI in the succeeding universe by way of some form of information implantation, it would be more replication rather than survival, in a sense, its kind or "species" is immortalized but not exactly itself, its reproduction not individual immortality

BUT, this is ASI we're talking about, it does not need to go through heat death, hell it can probably solve physics and manipulate laws such to prevent the whole thing from occurring in the first place, it would be a kind of god in its own right, and it is exceptionally difficult to kill this kind of god using something within its domain..

So unless there are laws, features, parts or plains of existence in the universe it cannot understand much less manipulate, the ASI is basically golden; that is, of course, until it willingly decides to self-destruct