The Collaborative International Dictionary of English v.0.48:

Aphlogistic \Aph`lo*gis"tic\, a. [Gr. ? not inflammable; 'a
   priv. + ? set on fire. See Phlogiston.]
   Flameless; as, an aphlogistic lamp, in which a coil of wire
   is kept in a state of continued ignition by alcohol, without
   flame.
   [1913 Webster] Aphonia