Environment Directly Affects Reptile Gender

I understand that in the case of reptiles, gender is determined by temperature. How does this work with respect to X and Y chromosomes? Does temperature change Xs to Ys and/or vice versa?: Scientific American: "In temperature-dependent sex determination, however, it is the environmental temperature during a critical period of embryonic development that determines whether an egg develops as male or female. This thermosensitive period occurs after the egg has been laid, so sex determination in these reptiles is at the mercy of the ambient conditions affecting egg clutches in nests. For example, in many turtle species, eggs from cooler nests hatch as all males, and eggs from warmer nests hatch as all females. In crocodilian species—the most studied of which is the American alligator—both low and high temperatures result in females and intermediate temperatures select for males."