INDISPENSABLE FALSE AXIOMS?

In 1824 Sadi Carnot deduced the (prototype of the) second law of
thermodynamics from two axioms; one of them turned out to be false in
the end:

The false axiom: "Heat is an indestructible substance that cannot be
converted into work in the heat engine."

There are texts in Carnot's book showing that in 1824 the false axiom
had already become suspicious to him. So there can be no doubt that
Carnot would have dispensed with it if he had seen the slightest
opportunity. There was no opportunity and any analysis of Carnot's
1824 argument would unequivocally show that. Then how can a FALSE
axiom be INDISPENSABLE for the deduction of a (presumably) true
conclusion? How about the following argument:

Premise: A false axiom CANNOT be indispensable for the deduction of a
true conclusion.

Conclusion: The prototype of the second law of thermodynamics deduced
by Carnot in 1824 is false.

Pentcho Valev