For example, a newspaper. In general, last week's newspaper is much less relevant than today's. I want to use it in a sentence like: "Since newspapers are ____ in nature, it's important to be notified the moment a new issue comes out." Temporal is the only thing I can think of, but not really since I don't want to emphasize the object's impermanence.
When English speakers can't think of a single word for something, they sometimes stick words together to make a phrase. That's the case with time-sensitive, which the Cambridge Dictionary helpfully defines:
time-sensitive adjective UK US used to describe a product that has to be delivered by a particular time, or information that is only useful for a particular period: We deliver high-value, time-sensitive goods like cars, computers and specialist chemicals. time-sensitive documents
The word ephemeral suggested by a commenter conveys the brevity of something's life span, but it fails to deliver an indication of value.
We can raise the stakes on time-sensitive (a newspaper, in the original post) to time-critical (in the case of a shipment of vaccine for an outbreak of gomps in a remote corner of Rumtifoo).
I see you did mention temporal, the first thing that came my mind was temporal relevance (of the news, I don't think that emphasises the object's impermanence).
You could also borrow the phrase time value from finance (i.e. the 'time value of money' - £1 in your hand today is worth more than the promise of £1 later).
You could riff on that idea without the jargon by talking about newspapers' waning/depreciating relevance.
Another phrase might be 'of the moment' or similar.