It is much the same as why your car can get hot when parked in the sun, but if you open the doors it cools down. The energy existed in the universe before it heated up your car, primary in the form of light, and still exists after it cools down, but is now spread out over a much larger volume.
The heat death theory basically says that eventually the energy in the universe will be completely uniformly distributed. The total amount of energy in the universe will remain constant, however, and, according to all current theories, has always been the same: only how it is distributed has changed.
Per the second law of thermodynamics, if the energy is evenly spread out, nothing useful can be done with it, thereby “killing” the universe.
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