Carnot's work came almost 50 years after Watt's development of his steam engine. Of course valuable, but not strictly necessary. One could argue that thermodynamics developed out of necessity for more efficient engines but it's not a strict prerequisite.
As another example the brothers Montgolfier weren't aware that heated air could lift their balloon because it had less density than cold air. They still managed to get it work.
As another example the brothers Montgolfier weren't aware that heated air could lift their balloon because it had less density than cold air. They still managed to get it work.