We know that by heating things up can make them explode. How about by cooling them down? For those of you who doubt that you can make something explode by cooling it, just grab some white erasers and liquid nitrogen. Then stand back.
Things explode because the contents inside them suddenly expand to be a great deal bigger than the shell that contains them. This is most easily done by heating the object. When water or solid turns to gas, it expands in volume. Putting liquid nitrogen or dry ice inside a sealed container and then leaving them around at room temperature will lead to an explosion. Even gas expands to the point where it will explode its container, if it heats up enough. This is why cooling something generally doesn't work to burst it. Cooling a substance makes it denser and more close together.
But what if, instead of expanding the stuff inside the container, you're shrinking the stuff outside? This is harder to do, but the effect is the same, which you'll see if you grab some white erasers and a container of liquid nitrogen. The erasers are made of rubber, which doesn't conduct heat very well. Cool down something made of metal, for example, and the heat will drain away in an efficient and orderly fashion. As soon as the heat has radiated out of the parts that are in direct contact with the liquid nitrogen, heat from the inside radiates outward - through efficient conduction - and get sucked out by the liquid nitrogen as well. The entire structure would cool. Put a rubber eraser in liquid nitrogen and, although the heat will radiate out of the parts in direct contact with the nitrogen, the heat will stay snug in the center. This is fine, except that we've already demonstrated that objects generally constrict as they cool. The outer surface constricts, the inner contents strain at the outer surface, and the entire thing is cooled until it explodes!