That would only happen if the universe was a closed system. If it is expanding, then the 2nd law doesn't directly apply. That's where people are getting this freezing to death, but not heat death.
What follows is something that is both very interesting and not very well known. Even if the universe was a closed system (so that heat could not escape into a continually expanding space) and it was eternal, then ultimate heat death would ultimately be avoided. That is, even under the very conditions it is normally thought to hold, it won't.
What people who haven't had any statistical mechanics classes don't generally realize, is that the second law boils down to the trivial statement: "That which is most likely to happen, is the most likely to happen."
To illustrate why this is, I'll need to give you a little better understanding of entropy.
Imagine a table with a bunch of coins lying on it all face up. Now you give the table a jolt so that all the coins bounce into the air and come back down in random orientations. Some face up some face down. Entropy increased here right? Right. If you had a billion pennies on the table, you might go so far as to call it a "law".
But now, say you carried this process out for an infinite length of time. What is to stop one from NEVER seeing that initial state of all heads popping back up? The answer is nothing. For every jolt you give the table there is a very small but very real probability to return it to its initial state. You don't see this (normally) in real life because it is a SMALL probablility. However, in an infinite amount of time, this probablility will inevitably pop up and entropy will DECREASE when that does.
This is essentially how heat transfer works in a closed system, but it's slightly more complicated. Little heat energy quanta in various molecules get exchanged at random with the neighbors of those molecules which do the same with their neighbors and so on.
Statistically, things even out and the heat spreads evenly and entropy increases to whatever maximum it has for the given system. BUT there is always (though prohibitively small to ever see in real life) real probablility that the system can revert back to its original state.
This is a probablility that MUST be realized if time were actually infinite, and the reason it must be realized is for the exact same reasons why heat transfer works in the first place. Probablilities.
What this all boils down to is that even if we were in a "heat death" state of the universe, we would eventually escape it by the same means that we arrived there.
To briefly touch on your other questions, heat death doesn't necessarily mean boiling to death or temperature, it's just that all the energy is evenly dispersed and can't be separated so as to do any actual work. Nothing could live in a heat death state because there is no way for a living thing to collect the energy needed to sustain itself.
For the universe escaping idea... that's a long response in itself, so I'll leave it alone. The short answer is no.
TO THE PERSON WHO DISPUTED MY RESPONSE
You DEFINITELY must take care when talking about ACTUAL infinities of microstates in the physical universe. You are just casually throwing out that the number of microstates is infinite, when you have no idea if that is true. Neither does Hawking. The only way that there are an infinite number of mico-states is that there are an infinite number of particles/quantons. THAT requires an infinite universe and THAT is NOT the universe where heat death is an issue and has nothing to do with what I was saying. I'm guessing you are thinking that the photons are infinitely divisible, but that's kind of what quantum mechanics is all about, they're not.
Also, what you said about the balls is inaccurate for actual infinities as 9 = 1+1+1+1+1+1+1+1+1, and if you sum up an infinite number of them you still just end up with 1+1+1+... the same as you would if you summed up an infinite number of 1's. If you are working with actual infinities, the very idea of how the second law works fundamentally breaks down.
Still, I do not know everything. If you have an actual source please list it. If you are just regurgitating something you saw in Discovery Magazine or wikipedia, then say that. Maybe you have a valid point, but I have severe doubts. I can see no way for there to be an actual infinite number of micro states without infinite energy and particles, and I can see no way to define a universe with infinite energy and particles as an isolated or closed system and that is where the second law applies.
Six Ideas: Unit T (intro to statistical mechanics)
The Direction of Time
-I think I might have thrown this one away, I can't find it.
AND A Brief History of Time
By Steven Hawking