prop driven aircraft are also give away IR signatures (their engines produce heat as they are combustion engines and have exhaust)...so that would improve anything
Jets don't rely on hot air either, jet engines heat air, but they don't need hot air. A piston engine generates heat and a jet engine generates heat, neither relies on hot air in the slightest.
Jet Hot air expands-> leaves jet -> produces thrust-> moves plane Prop Propeller spins-> produces thrust-> moves plane that kind of need Jet with no hot air produced= basically no engine