Correct usage of "a", "an" and "the" before "of"

The highest temperature of 39 degrees was recorded today. I am afraid I don't understand the usage of "of" in the sentence. It would be grateful if you could explain me.

Also, If there is a noun before or after "of", which one (a, an or the) would be used before the noun. Here is the example:

A number of "the" flies fly in or A number of flies fly in. Which one is correct?

"The" total number of A increased by 27% or "A" total number of A is increased by 27%.

It would be great if you could show me any online reference by any chance, please.