Leur ennemi ne sera pas que la chaleur accablante de cette région.
Turned this way, it seems like they will face only one multifaceted enemy, that will present itself as insubstantial oppressing heat, but also some other way that remained mysterious because the sentence ended unexpectedly after the presentation of the first form of the enemy. It would be appropriate in a fantastic or horror story, to present some uncanny entity in the vein of Sauron from The Lord of the Ring, but strange in a real life or realistic setting.
La chaleur accablante de cette région ne sera pas leur seule ennemie.
Now there seems to be several enemies, and the heat is a full entity by itself, not a mere facet of some major malevolent creature. It applies quite a bit better to reality as we know it.
So I suspect you indeed should have gone for the second version, though since you were referring to a conversation, I'm sure you were fully understood despite the slightly awkward formulation.
Deux exemples qui pourraient s'appliquer à nos cours de physique:
- La lumière n'est pas qu'une onde → elle est aussi une particule.
- Les ondes ne sont pas toutes lumière → le son aussi se propage via des ondes.