What is the maximum allowed temperature to cook onions saving the fructooligosaccharides?
To give some perspective on FOS (fructooligosaccharides) denaturation characteristics to sucrose (for a baseline since sucrose is a common molecule),


  FOS are water-soluble and their sweetness is 0.3-0.6 times that of sucrose, depending on the chemical structure and the degree of polymerization of the oligosaccharide. FOS are highly hygroscopic and their water holding capacity is greater than that of sucros. The viscosity of a FOS solution is higher than that of sucrose at the same concentration because the greater molecular weight of FOS. The enhanced viscosity of the gastrointestinal content may delay the rate of gastric emptying and the digestion and absorption of nutrients. Their thermal stability also is greater than of sucrose. FOS are highly stable in the normal range of food pH (4.0-7.0).


Source: https://www.ukessays.com/essays/biology/chemical-structure-of-fructooligosaccharides-biology-essay.php

This is comparing the FOS (fructooligosaccharides) to normal sucrose.  Specifically, this mentions that the thermal stability is greater than sucrose.

If sucrose has a decomposition temperature of 186°C (367 °F), when it starts to form caramelized onions, then it is safe to assume that you will be able to fry your onions in olive oil with a smoke point of 160°C without denaturing the FOS since FOS has a greater thermal stability.

Source for decomposition temperature of sucrose: https://en.wikipedia.org/wiki/Sucrose