The story of willowfine is roughly as well known as penicillin. The point is that in 1910-1920 people didn't carry NSAIDs in their purse and pop 400 mg when they felt a headache coming on or their back hurt. That's a big difference.
It's also worth noting that right at that point, the supply of aspirin was very limited due to phenol shortages caused by the war.
Human body temperature varies naturally by about 5 degrees F. This study is talking about a .4 degree change. At the very least, your body can definitely handle it. This is purely an interesting phenomenon that may not even be real.
Aspirin is very well-studied and definitely known to be very beneficial for your lifespan and quality of life. You should absolutely not throw away all that knowledge because it may be tangentially related to arbitrary theorizing (about inflammation) on a strange result on sketchy data from uncontrolled groups with unknowable biases. Medicine is proven to be good for you. Even if it does have unknown negative effects -even if this is an effect that we don't know about, that may not even be bad- you should not disregard medical wisdom for the sake of what you don't know.
Relatively speaking, it also has a fair low LD50. For a person around 150lb, 40 standard 325mg pills can be fatal. In fact you'll almost never, outside of hospital supply, find the 81mg chewable version in quantities higher than 36 in case children get a hold and think they're candy. Even then, a 2 year old downing a whole bottle would still be close to an LD50.
All in all, despite being extremely common and cheap to the point of nearly free ($10 for a year's daily supply) it is actually less safe than other NSAID class drugs. But then none of this stuff, strictly speaking, is "safe" if it is used outside of it's normal use parameters.