It's a mouthful, but it's not nearly as complicated as it sounds. Let's parse the title in the following points:
As we found out, the average temperature for each day of the year seems to fit an annual cycle. It may have to do with the rotation of the Earth around the Sun.
There appears to be a trend of increasing temperature. Some have called that global warming and blame industry and human beings in general for it. Without getting into a political discussion, let's assume that there is truth in this claim. Further, let's assume for now that this trend depends on the year. I know I will get into trouble for this, but let's also assume for now that the relation is based on a first-degree polynomial (a straight line).
For the sake of argument, let's claim that the previous two points together form a time-dependent mean. We will model what is left over as a linear combination of autoregressive lag components.