Hi Natasha,
When discussing thermodynamic stability, I look for the lowest energy species, as I find an easier way to parse things is:
High energy = low stability
low energy = high stability
when I think of molecular stability, I think the strength of intramolecular bonds - oxygen is stable, as is methanol, despite having very different boiling points. As a result, boiling point can't really predict if something is unreactive or stable.
What is more telling, is how much energy a molecule releases upon reaction - if a molecule releases a lot of energy after burning, it must have been in a high energy, unstable state prior to reaction.
As a result, we would expect a low energy compound to release relatively little energy upon combustion, as it can't really react to reach a lower energy state than it already is at.
Please let me know if this is unclear,
Katt