How long can a naked human survive on Mars?
Long story short, the astronaut probably wouldn't make it, and would first loose consciousness then suffocate.

There is a lot of myth and hollywood dramatization regarding this kind of thing. Here are some:


You will explode. This is just ridiculous. The skin is air tight (relatively speaking). It is also very elastic and can pull and bend quite a great deal before tearing. Through quite a few, equally durable, tissues, it is connected to the bones, which are unaffected by negative air pressure.
Your blood will boil. The circulatory system is also a closed system. It is not directly exposed to the environment. Also, the blood pressure in a healthy person is averaged around 100 mmHg and Earth's atmosphere at sea level is 700 mmHg. There is already a massive disparity, yet Earth's atmosphere doesn't go pouring into our veins at random. Likewise, the blood in a person's veins won't go pouring out into the atmosphere simply because the pressure is extremely low.
Any air in your lungs will be forcibly sucked out of you. Again, this is a closed system, if you hold your breath. As long as you don't try to breathe there is nothing forcing the air from your lungs.
Your eyes will be sucked from their sockets. Thank you Total Recall (the original) for this myth. The eyes are very firmly in place. You might feel a pull on them, but they aren't going anywhere.


Absolutely none of these would happen in the vacuum of space and certainly not on the Martian surface.

Here's what will happen:

Any liquid material on the surface of your body will vaporize. All sweat, saliva (if you open your mouth), water in the mucous, and tears on the eyes, will nearly instantly vaporize. It would be quite uncomfortable, especially the eyes, but very survivable. Long term exposure to a vacuum might damage the eyes eventually, but in this scenario there are far more pressing matters.

The negative pressure may also cause your eardrums to rupture. Try to imagine the feeling your ears get on the plane at 30 thousand feet times about 100. Since you can't close your ears, plugging them with your fingers may help, but likely just postpone the inevitable pressure disparity, which will lead to at least great discomfort and possible drum rupture.

If you had the chance, you should take a deep breath before jumping out and avoid trying to breathe at all costs. Opening your lungs for a breath would very quickly draw whatever breath you had in them out into the atmosphere and also vaporize any fluid that was in them. Considering the rapid pace of this event, you would surely have permanent damage from this and begin suffocating and will die in a minute or two unless you get medical attention. There seems to be conflict in the procedure for this, with some sources suggesting that emptying your lungs would be better to avoid this. Considering the astronaut in your example is about to do a 200 meter dash he is going to need all the O2 he can get.

The cold is also a treacherous factor. At -50C the heat from your body would dissipate so rapidly that it would likely be very debilitating, perhaps causing you to seize up and clutch your extremities to your chest. It would also be excruciatingly painful. It might cause you to fall into shock. In a total vacuum however, this does not exist. A vacuum is actually very insulating, but on Mars' what little atmosphere is there is enough for you to feel the chill.

The lack of oxygen and high CO2 would be what would eventually kill you. You would eventually try to breathe and loose consciousness within a breath or two (or you might loose consciousness first then your body would try to breathe naturally). Your body would try to keep you alive as long as possible by pumping your heart faster and increasing your blood pressure, but your heart would eventually fail and you would die within seconds after that.

Evaluating your particular scenario

There are first a few things about the scenario that seem unlikely.


The astronaut would not be naked. They remain in some of their protective gear in case of emergencies like this. He would have some protection against the cold if he had to run out without it.
Certain things like extinguishers are always nearby. The idea that one was unreachable is a little silly.
Space vehicles, shuttles, and buildings all are compartmentalized like a submarine. They could simply close off the affected areas.
Fire only burns in the presence of oxygen (with few exceptions). After being closed off, compartments can be decompressed, halting the fire immediately. They can then begin refilling them with breathable atmosphere. This poses the same vacuum problem if the astronaut is in the affected area, but he won't be trying to run across the surface naked. People have survived rapid decompressions before without a single injury, as listed in my second source, however, others have never regained consciousness.
Assuming you made it to the other building, they usually only open from the inside. So unless someone saw you coming and opened the door for you, your last minutes would be better spent desperately fighting the fire until it consumed you rather than banging on the neighbor's door.


But let's say all of this breaks down and poor Astronaut Joe finds himself making a mad, streaker's dash across the Martian surface.

We should assume that our astronaut is both quite athletic and knowledgeable about the environment outside of his shelter, knowing that he should take a deep breath before heading out, but literally has no time to grab a shirt, goggles, breathing mask, or anything. Just him and Mars.

If he's lucky, it's not too cold and he doesn't seize up and fall into the fetal position within a few steps. Let's say it's -20C, which is pretty darn cold, but tolerable for a minute or two. I next see him flailing across the surface, trying to run in Mars' low gravity (no easy task). He begins to loose vision as a cloud of steam of what should be tears pours from his dry eyes. His eyelids then begin to stick to his eyeballs because there is no longer any lubrication. He is desperate to reach the other building, and his movements get more and more erratic, as his body is rapidly using all of the available oxygen. All the while, he is still holding his breath, knowing that if he attempts to breathe he will likely collapse within seconds and perish. But the more he struggles to make it, the more his innate urge to breathe overpowers his conscious thought to prevent it. Eventually, against his own willpower, he gasps and attempts to inhale deeply. He takes two or three dying breaths, if they can be called that, then falls to the ground unconscious. He dies shortly after when his heart stops and his brain tissues die.

The whole ordeal lasts under 30 seconds and he is 100 meters at most away from his shelter. If he did get lucky and actually made it to the other building, he would likely have frostbite over much of his body, permanent damage to his eyes and ears, and possibly deadly exposure to cosmic rays.

The event would be very similar to being drug by a fishing line to the bottom of the sea and drowning.

Sources:

A fun questionnaire to see how long you would last in space
What really happens in a vacuum