There are difficulties with trying to do inference in this problem any
way you cut it. On the **conceptual** side, what is the population from
which these 365 temperatures might be thought of as an iid or simple random
sample? If the population you are interested in is 1975 in San Francisco,
we have all the data; there is *no uncertainty* about the mean temperature
of this population. If instead the population is some broader time period in
San Francisco, then we don't necessarily have a representative sample of
the temperatures across the whole time period -- all we have is a sample
clustered at one time point, 1975. What if there was a gradual warming or
cooling, for instance, over a period of years? We would not be able to
pick that up. If instead the population is 1975 in some broader region
than San Francisco, again we don't necessarily have a representative sample
of the temperature across the whole region -- all we have is a sample
clustered in one place, San Francisco. It is pretty hard to invent a
population from which these numbers can plausibly be regarded as an iid or
simple random sample.

Even if you thought things were Ok conceptually, there's a big **technical**
problem here. 365 iid draws from a population of temperatures would not
show the seasonal trend that you see in the picture provided with the
problem statement -- the plot shows a strong up-and-down pattern over
time, whereas with iid draws the picture would just look like random
fluctuations around an underlying mean temperature. Inference using the
usual iid machinery just is not appropriate here.