I don't think you understand what I said:
Previously the common thinking was that the universe would likely go in one of two directions - endless expansion or eventual contraction, the endless expansion resulting in a "death by cold", due to entropy, there would no longer be any transference of energy between objects and everything would simply be neutral. The other being contraction, which would eventually bring everything closer and closer together - resulting in a "death by heat", where too much energy would be too close together, eventually perhaps leading to another bang/expansion.
In this story, objects, or life as we know it (or can suppose it) would cease to exist due to freezing rather than burning. Death by cold. Not death by heat. Death by lack of heat, death due to entropy.
Now, of course, there are alternative theories that break these two older molds, but...yeah.