How does the heat death looks like from inside the system? As this answer points out, any human would first freeze rather than experience the heat death. However, assuming hypothetically that we could make some robot live at such low temperature (or even considering a theoretical observer whose perception rate depends on the speed of processes taking place inside its "body"), how the heat death would look like from its perspective? 
For example, if we could say that movie characters perceive things, playing using half speed is slow for us, but from their perspective everything behaves normally. We could pause the movie and then make it play again and they wouldn't even notice.
Is the heat death in any way similar? Or perhaps no such robot is possible because its components would dissolve first, hence, no (in a way) conscious process is able to observe their own heat death?
(I was trying searching here and elsewhere, but nothing came up. It's possible that I've used wrong search terms, in which case I would appreciate someone pointing me to the correct ones.)
Edit: For clarification, I'm interested most in what is observed as heat death happens (for example, just an $\varepsilon$ before it). After the heat death happens, as the name suggest, the universe has died, so no robot can do anything.
To use the movie example, suppose that we were to put a speedometer (displays a the current playing speed) inside the movie world which could be read by the characters. Then, if we were to play a movie slower and slower until stop, after the movie is paused the characters cannot move or do anything, in particular they cannot see the reading of the speedometer (similarly the robot cannot do anything interesting after the heat death). On the other hand, just before the stop their world would not be different from their perspective, only that the speedometer would read close to zero.
 A: I would say it looks like nothing. The heat death requires that the whole universe is thermodynamically homogeneous, and that the universe has reached its maximum entropy. This means that every thing becomes a disordered lump of very sparse matter, without anything to see whatsoever. It's as if the universe is in a state akin to the "chaotic nothingness" described in some (including Chinese) creation myths which, ironically, describes the birth instead of the end of the universe.
A: I think you have a fundamental misunderstanding of what the heat death really is. Any observer, whether they are a time traveler, observer from another universe, or whatever, would just see a lot of empty space.
The first thing to know is that the heat death is not a single event. The universe, after heat death, is dead in the sense that nothing is happening in it. It is just very uniform - everything is the same cold temperature (other than random fluctuations), and any existing matter is spread out. As the others have mentioned, this makes it impossible for life as we know it to exist - there is no way to increase external entropy in order to decrease internal entropy. However, a time traveler in a spaceship could pop in and live there with little difficulty.
The second, and probably more important, thing to understand is that the time scale is absolutely mind-boggling. As mentioned in the Wikipedia article, the heat death of the universe is going to happen on the scale of $10^{100}$ years in the future. You don't realize how long that really is. Here's an explanation of how large $8*10^{67}$ is:

Start a timer that will count down the number of seconds from 52! to 0. We're going to see how much fun we can have before the timer counts down all the way.
Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps. After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty. When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean.
Do this until the stack of paper reaches from the Earth to the Sun. Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063e67 more seconds to go. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385e67 seconds remaining. You’re just about a third of the way done.

Keep in mind that even this is far less than $10^{100}$. If you add removing Mt. Everest one ounce at a time and filling up the Grand Canyon one grain of sand at a time to the end of that chain, you are finally at the right scale.
By comparison, the last stars are going to burn out in somewhere around $10^{14}$ years.
So here's what it would look like - nothing. Lots of nothing, for a very, very, very, very, very, very, long time.
A: From a thermodynamical point of view, living beings are able to reduce their entropy by exporting entropy to the external world. This does not contradict the 2nd principle, since living beings are open systems. For this reason, in a thermodynamically homogeneous universe (heat death), no change in the entropy can occur, and consequently no living beings (nor sentient beings) can survive. 
But you asked about a non-living "robot", or whatever.
In this general case, observing the universe means that the robot has to acquire information from the external world. It has to modify its internal state in order to store this information (for example, a picture of the universe, a measure of some physical quantity). This change of the information stored in the internal state corresponds to a decrease of the internal entropy of the robot. 
But again in this case, one cannot produce a gradient of entropy in a thermodynamically homogeneous universe. This would contradict the 2nd principle of thermodynamics. 
One can say that the act of "observing" (which does imply a change in the information stored) the heat death is not compatible with the 2nd principle of thermodynamics.
Edit: Ok, let us suppose that the universe is thermodynamically homogeneous except for a very small region around the "robot", for a period of time $\epsilon$ before the heat death $t_0$, at which time the whole universe (including the "robot") is dead. It is a rather unprobable situation but let us assume so. At this point, what does the universe look like? All thermodynamical quantities are homogeneous, including temperature, density, and so on. Hence, there will be no recognizable structures (no stars no galaxies no anything) and all you could measure is a uniform and isotropic radiation at a temperature $T$ in all directions, similar to the cosmic microwave background. With the difference that the CMB that we measure today does reveal large-scale structures and it is not uniform in all directions. At the end of the day, the robot could describe the entire universe with a bunch of thermodynamical quantities, e.g., temperature and density.
What I've written is highly speculative anyway, it is not taken for granted that the universe will undergo heat death in the first place. There are many other scenarios, I think.
A: Lie down and fall asleep.  Right on the razor's edge between awake and asleep, look at what it all looks like.  See yourself and the world in unison, fading away... slowly, and at the same time instantaniously.  Then, in the morning, be thankful that your experience was merely that of falling asleep, and not a more permanent heat-death.
(The question is actually much more a philosophical question than a physics question, because it really involves the Qualia associated with heat-death.)
In theory one could define a "conscious" system which is scalable enough such that it retains its consciousness as one approaches the limit of heat death.  Fractaline structures could potentially do this (obviously they cease to function at heat death, we're just looking at the limit as you approach it).  Of course, whether one can claim such a system can "observe" the world is one of philosophy, not physics.
