Is there some specific reason to think that prions are harder to denature than other proteins? It seems like mad cow disease could also spread simply because meat is not normally cooked to ensure that 100% of the proteins in it are denatured.
Prions are essentially already denatured/unfolded. They are a more stable state of a normal protein that has biological function, and they interact with the "correctly" folded proteins to cause them to denature into additional prions. Often denaturing a prion means actually breaking apart the protein into fragments or amino acids, because it is already at the most stable/denatured state. This is also why they are so persistent in nature and so hard to remove from surfaces. Apparently gas plasma sterilization is a promising possibility. (this seems like an ok overview of the challenges: https://pubmed.ncbi.nlm.nih.gov/21271212/). Current procedures include things like autoclaving in 121C sodium hydroxide for 30 minutes. Definitely not something that fully cooking will inactivate.
In addition prions seem to contain disulfide bonds, which tend to make proteins even more stable. (RNAse for example has them and is notoriously hard to get rid off unless you treat it with essentially H2S).
I haven't found a source for that, but according to my bio teacher mad cow disease started, because they decided to lower the temperature to pretreat animal waste (such as bones and brain matter...) which then ended up in what cows get fed with. Wikipedia mentioned nowadays they simply leave out the bones and brain from the food.
