I think you’re confusing different types of radiation, which is fair because Physicists confusingly named different things “radiation”.
So-called ‘black-body radiation’ or ‘thermal radiation’ is the electromagnetic radiation that all objects emit when they have a temperature above absolute zero. Generally objects at room temperature emit in the infrared spectrum, which is why IR cameras work in the dark and can be used to tell how hot something is. But very hot things emit in the visible spectrum, which is why metal for example glows red-hot when heated.
Radioactive materials on the other hand radiate ionizing radiation as part of their decay. The atoms in the material are unstable, and want to transform into more stable atoms by losing protons or neutrons. And they do this by emitting Alpha particles (two protons and two neutrons bound together), Beta particles (which are emitted when a neutron in the nucleus transforms into a proton) and Gamma rays (which is high-energy EM radiation emitted by the nucleus when it transitions from a high-energy arrangement to a lower one).
So the temperature of the material doesn’t really have much to do with the radiation emitted by radioactive materials. It’s a different type of radiation. Alpha and Beta particles are, uh, particles, not EM radiation at all, which just confusingly got called “radiation” because they when they were discovered physicists noted they were kinda similar to the recently discovered x-rays which were known to be a type of radiation. They were even briefly known as “alpha rays” and “beta rays”. Gamma radiation is EM radiation, so it is the same type of radiation as thermal radiation, except not really because gamma rays are super energetic while most thermal radiation is in the relatively un-energetic infrared spectrum
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