"The calculations" rr speaks of require various assumed constants, including the very unknown mass of the universe. There is no way to truly know if the Universe will eventually collapse or not, because we have no idea of how massive it is, how old it is, or how old it will be before reaching either heat death or the point of collapse towards singularity. We can easily talk about how it's currently expanding and even accelerating away from itself in every direction right now, but who's to say that this ten-twenty billion year point is but an infinitesimal fraction of the lifetime of the Universe; who's to say that this is still the big bang, the Universe is still exploding, as we speak -- it simply has not cooled down enough for us to really understand what will happen to it 10^1000 bazillion years from now.
Most heat death supporters use the laws of thermodynamics to support their claims. I use the same laws to argue against them. The second law of themrodynamics states that entropy will "always" increase and temperature will always decrease as energy is distributed outward (until it reaches a point where everything is of equal temperature); yet we are also told that a state of absolute zero can never exist. We are told that matter will gradually thin out and dissipate until it has run out of energy (or it will infinitely approach running completely out of energy, but never reach it), that there will be no more usable energy left to do work.
Another thing we don't know is if there truly is a fundamental particle. If not, then there are infinite possibilities of low-energy particles that can be the last tiny bits, nearly motionless particles to move towards the state of heat death. The temperature gradient would inevitably drive temperature to approach absolute zero as entropy increased and the Universe expanded ever more, cooling it down by increasing its volume.
How many times can matter divide (or degrade) before it completely decays into nothingness? As the laws of thermodynamics state, neither matter or energy can be created or destroyed, they can simply be transformed into different proportions of each other. Pure annihilation reactions involving anti-matter inevitably create high-energy photons, often gamma rays (e.g. when a positron and electron escape from a black hole and create two gamma rays of Hawking Radiation). I contend that photons represent the physical manifestation of entropy; they travel at the speed of light, faster than anything else, making them useless unless they smack right into something, yet they are always traveling "away" from their origin. A very small number of them collide with matter and lose some of their energy, but inevitably continue on their course, slightly altered but still "away" from their origin (except in a black hole, of course). Every chemical reaction creates some light; often it is re-absorbed by the electrons in the chemicals themselves, but there will always be some loss, sometimes visible, sometimes not. "Heat" is light; specifically the infrared spectrum.
I also contend, just as physicists "contend" when they assume some arbitrary quantity of matter into their calculations, that during the big bang some immensely monstrous quantity of energy was instantly transformed into light, which we now faintly observe as cosmic background radiation. We do know that a significantly large portion (90% or so) of the remaining physical matter was quickly cooled (but by what scale?) and converted into hydrogen, a gas that conveniently burns cleanly to produce prodigious amounts of light. The observable background radiation that seems to radiate away in all directions may have been all gamma rays at some point, but as light travels it ever-so-slowly slides down the spectrum. Who knows, maybe 99.9999999% of the Universe's mass was instantly lost in the form of entropy, yet it's still going to take many, many, many, many aeons, epochs, millennia, bazillion years or whatever (it's all arbitrary in our can't-comprehend-a-million minds) for the Universe to use up whatever smidgen of energy it still has. And if 99% of its mass is converted into light, there will be a continual pull of gravity from the outer reaches of the Universe towards whatever matter remains. Light is affected by gravity and therefore has a gravity of its own; for all we know the acceleration of the expansion of the Universe is driven by cumulative gravitional forces exerted by mere photons, or by photons released by "virtual particle" reactions found in "empty space."
For all we know, the laws of thermodynamics may change at some point. If they don't, the final result is a Universe with no usable energy, and therefore no motion (even photons decay), with an impossibly low temperature. No energy means no matter means no laws of thermodynamics. So do they (the laws) collapse, or do they reverse? NO ONE KNOWS, DAMNIT. If everything actually reaches a state of perfectly equal temperature, even entropy (heat) itself is destroyed, as to stop a photon is to "annihilate" it, and to equalize all temperature is to halt all heat transfer. Both useful and usable energy are gone, leaving...nothing. And we all (think we) know that nothing is a state of existence just begging to be everything.