Regarding 49 CFR 830, what is considered an in-flight fire?
No, there does not need to be visible plasma, and smoke alone is enough to constitute a fire onboard an aircraft.

FAA Advisory Circular 120-80A contains the following definitions that indicate that a visible flame is not the only definition meaning "fire" pertaining to aircraft.  In my experience, it's reasonable to expect that the FAA's definitions in this case would fall in line with the NTSB's definitions.

Hidden Fires:


  Fires that are “hidden” are not readily accessible, may be difficult
  to locate, and are more challenging to extinguish. Some examples of
  hidden fires would be fires behind sidewall paneling or in overhead
  areas.


Smoldering Fire:


  Combustion without a visible flame and a slow combustion rate are
  characteristics of a smoldering fire. A smoldering fire left
  unattended or an incompletely extinguished fire can ignite and grow
  into a larger, uncontrollable fire in a short time.


Suppressed Fire:


  A fire that has been partially extinguished which may or may not have
  visible flames. A suppressed fire, if not extinguished, may
  reestablish itself and grow into a larger, uncontrollable fire in a
  short period of time.