Hello there!
By the Railway Side by Alice Meynell is set in Italy, where the author spent most of her childhood.
The full paragraph is as follows: "My train drew near to the Via Reggio platform on a day between two of the harvests of a hot September; the sea was burning blue, and there were a sombreness and a gravity in the very excesses of the sun as his fires brooded deeply over the serried, hardy, shabby, seaside ilex-woods."
The line you mentioned implies a very hot, very humid summer day, the kind that is so hot that it becomes difficult to both breathe and move. It's a classic depiction of the peak of the season, and the "burning blue sea" emphasizes the feeling of summertime.
I hope this helps you!
