I don't think this type of plot has a name, but as the legend shows, the shades of gray represents the quantile distribution of repeated temperature measurements, taken on the same calendar day over multiple years, and plotted as time-sequence. It is basically a variation on jamming together a sequence of 92 box-and-whisker plots, placing them each above the date on the x-axis.
I am struggling to quantify and describe the trends that I can see, because this plot combines two types of trend analysis. Time series can use simple language like "rising" and "falling"; distribution plots can use specific words like "skew". But how do I describe the trends in a plot like this where each point on the time-axis has a different spread and skew? For example, there's a spot in late September with a light-gray downward peak spanning several days--how would I describe that peak?