I have checked a couple of my meteorology books at home.
The published mean temperatures for FL350 in a tropical airmass like over Singapore range fairly close to -45 C be it summer or winter.
For an arctic airmass I found summer temperatures of about -45 to -47 C in two publications, whereas winter temperatures where stated as -58 to -60 C.
Like Mad (Flt) Scientist said, the average temperature at the north pole is lower than over Singapore.