I have researched for the proper NPK ratio for fertilizing a bluegrass lawn
here in Toronto, ON, CAN.

I am not sure if I should be too concerned about the theoretical variation
to the fertilizer's NPK ratio to use at different times due to the season's
temperature change. I have not yet found any info on this adjustment.

All the info I can find is a 3-1-2 ratio (e.g. 21-6-12), probably because
the sites I found for KBG are all in the US, where there are not substantial
temp changes or seasons.

Do I need more specific info about how the NPK ratio changed depending on
the time of the year?

I believe I have found the correct times of the year, at least, though
(possibly off a little):

Late winter/early spring (April-Early May)

Late spring/early summer (Mid June)

Late summer (Early Sept)

Fall (Late Oct./Early Nov)