[okonomiyaki3000]

But what if your Big Bang was only a local bang among an infinite number of bangs so far apart from one another that the light from any of them would take 100s of billions of your earth years to reach its nearest neighbor. Then, even now, they are all expanding toward each other with no way for any of their passengers to know it. You won't need to worry about a heat death or a cold death, you will have a death by collision and probably some kind of rebirth to follow.