Without some other problem, it would be my opinion, that a 30 amp load on #14 would be unlikely to raise the temperature of the wire itself to the point where it could ignite ordinary building construction or furnishing materials, at least not over a short time. Pyrolysis may over time lower the ignition point of the material enough that the #14 carrying 30 amps could ignite the materials. #14 carrying 34 amps will not operate at a temperature that exceeds 302?F.
However this high conductor operating temperature will cause insulation damage and may result in an arcing condition that could start a fire.
That's what makes me wonder, and I breaks down into 3 questions IMO:
1. At what point will NM-B exceed 90*C in,
a. a wooden framed wall with no insulation
b. a wooden framed home with R-14 fiber glass bat (for example) on an outside wall.
2. At what point do temperatures have to be high enough (or long enough) to lower the ignition temperature of wood.
3. At what point will current heat NM-B to the point a fire will start on fresh wood factoring 1(a) and 2(b)
Of course my thinking isn't perfect, more an educated guess.
Quite unlikely as the insulation of nearly all 14 gauge conductors can handle 25 amps from table 310.16. I imagine most fires are from loose connections that arc and/or build up heat and that one in a thousand spark that lands in the perfect spot and smolders and eventually catches something on fire rather than going out.
You know, that makes a lot of sense now that I think about it.