'Temporality' (as an unqualified noun) is too broad and ill-defined to be the essence of a tool. A tool isn't defined merely by the fact that it has a relationship to time; a tool is defined by the fact that it binds a specific effect to a chosen time. For example, consider what happens when a hunter captures and kills a prey animal. The hunter has to get past the outer integumentary (skin, shell, etc) to reach the parts of the animal that can be eaten. This can be done in three ways:

• The hunter uses teeth, claws, fingers, or other body parts to tear through the integument (the typical approach of natural-world predators)
• The hunter finds an object in the immediate environment that has the effect of breaking through the integument (a sharp stone, a pointy stick, something heavy that can smack a shell…)
• The hunter carries around a reusable object that is designed to break through the integument (a fabricated knife or hammer, etc…)

In the first case the hunter uses what it has to-hand to produce an immediate effect; in the second case the hunter looks around to find something that will produce an effect in the near future, and discards the object after; in the the third case the hunter carries an object that will produce an effect on demand, at any given and desired moment. This last principle — the ability to produce a specific effect on demand — is what constitutes a tool.

Bataille isn't wrong by any means, but I think he might be overstating things. I mean, we can think about a hat as a tool for keeping rain or sun off one's head, but socially and historically hats are used in far more diverse cultural and psychosocial ways: as beauty statements, to display group affiliation, to indicate social class or personality characteristics… I think we want to restrict the concept of 'tools' to items that are specifically constructed to produce particular effects on demand, and not broaden it to ambivalent objects that can be used in multiple ways for multiple purposes. Such ambivalent objects are more like the 'found' objects in the second bullet point: things we find in our immediate environment that we use for momentary purposes and then release. I mean, if we buy a hat at a thrift store so we can go to a halloween party as Michael Jackson, it's not really a tool in the same sense as a hat we bought to wear in the rain. But maybe I'm being philosophically picky…