My discussion here on temperatures refers only to Gouldian and Society Finches, the two species that I breed. Society finches are much more tolerant of colder temperatures than Gouldian finches, and while my Society finches are never exposed to temperatures below 55F, I am told by many a British breeder that they can tolerate 45F if the adjustment is made slowly. Alternatively, you can keep a heat lamp outside the cage near a perch to help them stay warm.
Gouldian finches come from the north of Australia, the warmest part of the country.
Again, however, I would say they are most happy at 65-80F, although I let my bird room go to 90F when breeding season is approaching. Because the bird room is in the basement it never exceeds 90F anyway. What is important is that any change in temperature be done gradually so as to let the birds adjust and not shock them. Sudden downward temperatures are much more dangerous than rises in temperature.