Blue light has a higher frequency than red light, and blue flames are warmer than red flames. Are there a connection? 
Good call, and an interesting observation - did you look into it?
yes
I’m trying to find something about it but it’s really hard.
Yes, but not necessarily. Simply put: as the heat energy goes up, so does the energy of the light. More energy means higher frequency, which in the visible spectrum means towards blue and away from red.
The colour of the flame also depends on which chemicals are being burnt, though. Some yellow flames can be hotter than some blue.
the sky can be blue or red too.
O:
But that has to do with reflections…
It becomes reddish at night, when its colder.
Maybe there are connections here too?