As is often the case, this explanation fails to take cosmological expansion into account. An expanding universe is a cooling one. The explanation is correct as

As is often the case, this explanation fails to take cosmological expansion into account. An expanding universe is a cooling one. The explanation is correct as far as it goes, but failing to take expansion into account either dates the explanation or fails to evaluate a factor that's a bit more complex than relying on the finite age of the universe.