Imagine a chain that is said to undergo a coil-globule transition at temperature Tc. Let's say we are just above Tc, and the chain shows a preference for a collapsed state. If the temperature were to continue to rise, the previously unfavorable states are also accessible. So at one point, the chain will cease to be in a globular/collapsed state and expand again. At infinite temperature, it effectively becomes an ideal gas.

My question is, is there a way to identify this second temperature where this expansion takes place? By this logic, the radius of gyration for a chain that shows coil-globule transition must show a local minima, and then revert to some higher radius of gyration.

what are the order parameters one must keep track of to capture this coil-globule transition, and then the eventual expansion of the chain due to high thermal energy of the environment?