Would they bring the bodies back for burial? If so, then the same situation may happen, especially given that the Thing would defrost rather quickly, if we go by the prequel, where it reanimated in about 2 days after being exposed to air. If they take the body off Antarctica, everything's still pretty screwed.
Actual worst-case scenario is where Childs is the Thing, and by the time rescue arrives, Macready's frozen to death but Childs has 'miraculously' survived. They take him back home, he tells some story that leaves out any mention of the Thing, and humanity is now guaranteed assimillation fodder.
The thing would not be able to survive that long. With the radio dead (not an uncommon thing in the Antarctics back then either) it could be weeks or even months before someone notices something might be amiss and redirects a plane. Maybe.
It can certainly survive being frozen though, albeit in hibernation.