The astronauts lives were apparently saved by the warm Plutonium battery powering the Lunar Module's scientific equipment (not exactly sure how though).
EDIT: I know what Radioisotope Thermoelectric Generators are, but not why the warm battery saved Apollo 13.
Also, alpha particles have almost no penetrative power in human tissue so they're harmless as long as the source isn't inside of you. Pu238 is almost exclusively an alpha emitter, so it's completely safe to handle for extended periods, at least radiologically. It puts off a ton of heat and is chemically really toxic though. I've dealt with it in the lab before, it's relatively harmless as far as nuclear sources go. It's not suited for weapons either, so it isn't directly a proliferation concern, though producing it is because it is related to weapons grade production. You don't see it used very often mostly because it can only be made in a specially configured reactor, so it's not exactly common.
http://en.wikipedia.org/wiki/Radioisotope_thermoelectric_gen...
The LEM (Lunar Excursion Module) did carry an RTG (Radioisotope Thermoelectric Generator) -- but this was for the ALSEP (Apollo Lunar Surface Experiment Package), which is what the training photograph shows Lovell carrying. The instruments were stored in an equipment bay and weren't even accessible from inside the LEM, and weren't relevant to navigation or communications anyway. The heat output of the RTG was not intended for life support, nor for keeping any LEM systems within safe operating temperatures. I am at a loss as to how plutonium was relevant to the astronaut's survival.
What is an interesting story is the fact that the Apollo 13 RTG is now resting at the bottom of the Tonga Trench in the Pacific Ocean, since the LEM re-entered the Earth's atmosphere after it was jettisoned prior to reentry: http://www.spacesafetymagazine.com/aerospace-engineering/nuc...
Clearly the plutonium heat output was never intended to heat the LEM during ordinary operation, since not all missions carried such experimental apparatus - presumably had the mission gone to plan the normal LEM heaters would have run on a lower duty cycle to compensate for the extra heat input from the plutonium cargo.
I agree that it's a badly written article that doesn't actually follow through on the title, so the above is purely guesswork.
https://www.dropbox.com/s/02px58fhbz0gigt/apollo13.pdf?dl=0
I doubt there would have been much thermal path from the fuel element back into the LM itself - indeed the mount would probably have been designed to minimise that flow since the problem is normally how to reject heat from a spacecraft, rather than absorb it. The story just seems a tag to discuss plutonium.
