Can ordinary civilians feasibly measure, for example, global trends in mean temperature without relying on the data of others?

No, but the literature is open for you to read. Thus you can judge the stated reasoning for yourself. You can also assess how many independent groups are making the same (or closely related) claim.

If only one person claims X then it might be fraud. If large numbers of seemingly unrelated people all claim X then you're forced to decide between X and a global conspiracy to misrepresent X.

To your example. Importantly, even if you deemed one of the global mean temperature datasets to be untrustworthy there are other related (but different) datasets. There are also other pieces of evidence related to the downstream claims that don't look directly at temperature.