Is there an upper limit to the "room temperature" at which eggs should be stored?
100°C would definitely be too high.

145°F/63°C -- Egg whites begin to thicken 
Same link:


  Keep in mind salmonella is killed instantly when subjected to a temperature of 165° F.


I think the limiting factor for letting eggs sit out is going to be salmonella growth rate. Looks like that maxes out at 19 degrees C (66°F).
Knowing that, I'd refrigerate.