First, specifying format in this question
I will be giving temperature ranges that sometimes appear backwards. This is because I am listing average temperature ranges from southern to northern latitudes. My landmasses are mostly located from the equator to the South pole. Therefore, my civilizations, who will mostly live in equatorial and temperate regions, will probably orient South to where more land exists. To the North there is nothing but ocean for thousands of kilometers.
Relevant planetary and solar specifications
I have a planet, Jasmi, with a 31.1 degree axial tilt. It's located in a relatively Mars-like orbit of 1.55 AU around an F7 type star, Xat, with surface temperature 6414 K, mass 1.21 MSol, radius 1.15 RSol, and luminosity 2.01 LSol. My greenhouse effect accounts for 33.08 K of my planet's average temperature.
In a previous version of this question, I had far too low an average planetary temperature to sustain anything like Earth-like plant life. I significantly increased my star's luminosity to compensate for the temperature, changing it from an F0 to an F7 spectral class.
Temperature variations in the tropics
Shagomir's Planet Calculator Pro gives average yearly temperatures in the tropics of 13.85-16.85 degrees C. Obviously my tropical temperatures don't change much throughout the year compared to the rest of my planet; that's what makes them tropics in a latitudinal sense. They do vary much more than Earth's, though. In the Northern summer, my tropics experience temperatures on average of 0.85 - 20.85 degrees C; in the Northern winter, my tropics experience temperatures on average of 25.85 - 4.85 degrees C. This gives an average yearly range of 25 - 16 degrees C.
My poles, as you might expect, are much more extreme.
My South pole has a yearly average of -25.15 - 0.85 degrees C, but in its summer it is 35.85 - 14.85 degrees C on average and in its winter it is -51.15 - -27.15 degrees C on average, giving an average yearly temperature swing of 87 - 42 degrees C.
My North pole is similar but less extreme in Shagomir's model for some reason: its yearly average is -26.15 - 0.85 degrees C, but in its summer it is 10.85 - 31.85 degrees C on average and in its winter it is -51.15 - -26.15 degrees C on average, giving it an average yearly temperature swing of 25 - 27 degrees C.
Given all this, my question:
My year is 640 Earth days long. Therefore each global "season," or sidereal year/4, is 160 Earth days, or 5.26 Earth months. Keeping this in mind, what biomes and climate classifications should I be roughly looking at in my poles and tropics?