A and B are base-α digits from 1 to α-1. Determine all triplets (A,B,α) with 2 ≤ α ≤ 36 that satisfy this relationship:

(AB)_{base α} degrees Celsius
= (BA)_{base α} degrees Fahrenheit

Notes:
(1) F = (9/5)*C + 32_{base 10}, where F denotes degree(s) Fahrenheit and C denotes degrees Celsius.
(2) Each of AB and BA denotes concatenation of digits.
(3) α is a positive integer.