If a nuclear reactor was running today and shutdown tomorrow, the spent/used fuel rods have to be stored under water at a certain temperature to keep them from melting down.

Side note: I have taken a public visitor tour of my local nuclear plant, Byron Nuclear Plant, and they are very careful the way they word their sentences. I do not believe it is by chance that you can't get them to use the term meltdown, regardless of what question you ask.

Spent fuel rods must stay in cooling pools (spent fuel pools) for about 5 years before they can be exposed to the air without starting a chain reaction. Here is a news quote to support this statement.



NEWS SOURCE: http://www.enewscourier.com/news/local_news/browns-ferry-nuclear-plant-begins-dry-storage-of-used-fuel/article_d14f35be-2a89-11e5-9c6a-571e48c189b3.html

Nuclear expert Arnie Gundersen says it best in this short audio clip:

https://www.youtube.com/watch?v=L4vFSNQvwNo