Not quite the case at all.... you are generalizing far far far to much here.. Both FLG and SPG can actually handle low temps to a point and the genetics and location of a particular SPG can in fact make a HUGE difference in the fish's tolerances and condition to varied Temps.. Broad native range things really mean nothing.. it is capture locality (or Broodstock locality) of a given fish that does. SNG and LNG are also notorious for this...
x2.
I know that a lot of people overlook the fact that Florida gars have been introduced as far north as southern Canada which certainly is further north than most people would expect them to be able to successfully survive year-round. However, I don't know the background behind those particular gars, so I can't comment on the effect that genetics & locality had on said introductions outside of their native range.