Definition:
"Spent fuel - Fuel elements that have been removed from a reactor after use because they contain too little fissile and fertile material and too high a concentration of unwanted radioactive by-products to sustain reactor operation. Spent fuel is both thermally and radioactively hot."
http://www.exportcontrols.org/glossary.html

Other things from above ref:
"Hot cell - Shielded room with remote handling equipment where highly radioactive materials can be safely examined and processed. Hot cells are typically used to handle and inspect spent reactor fuel or targets."

Oh, another item found under Google { "radioactively hot" + meaning }
November/December 1978
THE PROBLEM OF ATOMIC WASTE
...
"Uranium 235, for example, decays in a long series of steps that include the radioactive isotopes radium 226, radon 222, and polonium 218. The end result, finally, is the chemically stable, non"hot", lead 206.

The process of this breakdown is statistically predictable, even though the instant at which a single nucleus will be spontaneously transformed isn't. For this reason, atomic decay is measured in "half-lives", which indicate the time needed for one-half of the billions of atoms in a small quantity of material to undergo this transformation.

Let's take an example: One of the major short-lived isotopes in used nuclear fuel elements—iodine 131—has a half-life of 8.1 days. This means that, when 8.1 days have passed from any given time, half of the iodine 131 will be gone. After 16.2 days, only a quarter of the original quantity of isotope will be left . . . only one-eighth after 24.3 days . . . and so on. A period of 20 half-lives (which is less than six months in the case of iodine 131) will reduce the original radioactive isotope to one millionth of its initial mass.

You can see, then, that if all fission products had half-lives of about a week, the storage of these wastes wouldn't present much of a problem. They could simply be held at powerplant sites for a. year or so, and could then be disposed of in any way suitable to their chemical characteristics. Residual radioactivity would be—by that time—practically nonexistent.

Unfortunately, however, many of the fission products regularly produced in nuclear reactors have extremely long half-lives. Those of strontium 90 and cesium 137 are 28 and 30 years respectively . . . which means that these isotopes would have to be stored for 1,000 years before their radioactivity could be safely ignored. And plutonium 239, which is formed in reactors by the non-fission absorption of neutrons into uranium 238, has a half-life of 24,400 years. This material, in short, should be kept out of the environment for at least one-half million years . . . which is something on the order of 100 times longer than the human race has been recording its history! "
http://www.motherearthnews.com/Nature-and-Environment/1978-11-01/Ecoscience.aspx

Anyway, there isn't much of problem from any of the thermal heat from spent rods. The problem is they are radioactive. I don't think the links above are particularly informative or accurate, particularly this part:
"However, when the uranium atoms split they create fragments (called "fission products"), and the waste problem begins. The fragments, for example, contaminate the reactor's fuel rods so badly that the rods must be replaced about once a year. (This replacement is necessary because the fission products "poison" the chain reaction by absorbing neutrons without fissioning. The trapped neutrons are then unable to sustain the "atomic" reaction.)"

To say it's inaccurate, because after about a year the energy of the fuel is used up, rather than "posioned", if it was simply a problem of fuel being "posioned" then solutions to this be solved. Though "posioning" could a factor involved rather than "the problem".