Question: It's 2016, but for some reason, the Cold War never ended. You've been inspired by your (for some inexplicable reason) favorite movie, Indiana Jones 4, to start a new business: building refrigerators. However, the market is so saturated that in order to distinguish yourself with a nice marketing campaign, you decide to make them **NUKEPROOF!** 

The refrigerator should be:

1. Usable as a real refrigerator would be.
2. No bigger than standard double door refrigerator, so no room-sized walk-in refrigerator. Though, you *can* add some additional size for additional armor, for example, in **reasonable** margins, so nothing like 10 meters of iron from one side.
3. Protect one person from up to 1.2 megatonnes of a TNT nuke at a minimum distance of 2 km from the explosion.

How are you going to design it and what materials are you going to use?

Answer: 
GrinningX has quite a good answer but I would like to amend it slightly. The stats quoted appear to refer to a ground burst. Ground bursts are not thought to be targeted against cities because air bursts are more damaging to them. Ground bursts are expected to be used against hardened targets like ICBM silos. 

However, if a 1.2MT ground burst did occur in your city it the fridge owner would die for sure. Ground bursts generate enormous quantities of fallout. (Air bursts generate almost no fallout.) Fallout is created when energetic neutrons in the fireball touch heavy matter, converting it into unstable isotopes. Air burst neutrons interact with gasses, and the radioactive isotopes they make from this gas tends to stay aloft. 

The fallout from such a ground burst would be lethal for weeks to months - far too long to be hiding inside a refrigerator. 

On the other hand, an air burst produces almost no radiation on the ground (neither prompt nor fallout) so the radiation shielding would be largely unneeded. The most important need would be (in this following order of events) 1) protection from the flash (just being inside your house and away from windows is probably good enough), 2) protection from blast (sturdy steel construction and being securely bolted to a sturdy foundation would keep you alive), 3) protection from the heat and fumes from your house burning down, and 4) a mechanism to allow you to exit the fridge even though it has been buried by the debris of your house. Numbers 3 and 4 are quite a bit more difficult and complicated than 1 and 2. 

For surviving the fire, maybe some kind of hand-cranked air pump which pulled air in from outside and percolated it through a container of water (to cool the air and remove smoke)? That would help, but would not do anything to reduce carbon monoxide or lethal carbon dioxide levels. Heat would be less of a problem. Fridges are designed to be insulated, so just make sure the gaskets are fire resistant and increase the R value enough to survive. 

I'm honestly not sure how to handle egress. It's hard to guess what debris will be on the fridge and how it will be shaped. I don't have any good ideas for this one.
While the it's-not-possible answers are correct for the question you intended to ask lets try another approach:

For colder climates it's technically possible (but economic insanity) to build a refrigerator that contains no cooling element at all. Lets make the Green Fridge (tm):

No ozone-destroying Freon!
No toxic ammonia!
No risk of incomplete combustion of the propane causing CO poisoning!
Uses far less electricity than a normal refrigerator!
You'll be safe against anything less than a direct hit by a nuke!

Dig a big, deep hole. In the hole we put a large, very well insulated, very strong walk-in cooled space. Note that this will be at at least the sub-basement level, ideally it would be accessed by stairs or a ramp going down so as to minimize the air spill when the door is opened. There are two holes in the ceiling of the cooled space.

Above the cooled space, separated by the insulation layer is a large concrete box. One of the holes from the ceiling connects to a U-shaped pipe (so the opening points down) in one corner of the box, the other to a pipe in the opposite corner that connects to the top, again with a U on the end. There is a large bimetallic thermometer on the first pipe that opens or closes a baffle in the pipe. There also must be a drain for the box.

A pipe heading up goes into the third corner of the box, the box is filled with large gravel, a pipe is added in the last corner and it's roofed over and likewise very well insulated. Pipe #3 is insulated and extended to a surface air intake. There is a fan in this pipe (the only powered component in the whole thing!) that turns on when the outside air is colder than the air in the box. The final pipe vents back to the surface, ideally after running a bit through the ground first to dump its cold into the soil.

Now the whole thing is covered over except for the vent pipes and however you plan to get to your storage space. You want some feet of dirt and then a moisture barrier layer and more dirt.

Assuming you sized it big enough and the winters are cold enough this will work--you get a cold space for no more operating costs than running a fan in the winter.

Note that so long as you are dealing with an airburst this should survive anything, although escape might be problematic. You have basically perfect radiation shielding, the only modification you'll need to make to ride out the nuke attack is to add a supply of compressed air to use while the firestorm burns overhead.

(Note: In practice you would put the cold space on the bottom and use a fan to bring up the air, I was going for ultimate green. Also, the thermal mass needed is simply too great to be worth it. However, a related idea is in actual use by some people: Bury your house as indicated, run the air feeds through enough ground and you can climate-control your house with nothing but a fan. While the total heating/cooling needed is a lot greater the outside air will be in the right direction far more often and the natural ground temperature isn't too far below what you want for your house anyway.)