If I plant arugula, parsley, or cilantro during very cool or cold weather, they begin to seed with onset of the first warm weather. All three of those which were overwintered this year are either blooming or showing signs of developing flower stalks. I use a succession of plantings, with the last being planted near summer's end. Those always overwinter and are very productive when the winters are mild, with no hard freezes into the low 20's.
So yes, cold followed by warm weather does tend to trigger flowering in some plants. All three of the above are biennial plants so perhaps this is mostly a problem with biennials, though I've found that annual lettuce plants also tend to go to seed more readily if they were planted very early during cold weather. Just thinking of it from a biennials point of view, it is usually a warm growth followed by cold followed again by warm then seeding. So the trigger must be the cold followed by warm.
This is one reason that I rarely buy parsley or cilantro from a nursery for transplant. Those plants will often go to seed very early in the season. The outcome is totally dependent upon the growing conditions when the seeds were started and young plants developed.