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.