  We study the problem of high temperature Bose-Einstein condensation (BEC) of
atom-light polaritons in a waveguide cavity appearing due to interaction of
two-level atoms with (non-resonant) quantized optical radiation, in the strong
coupling regime, in the presence of optical collisions (OCs) with buffer gas
particles. Specifically, we propose a special biconical waveguide cavity (BWC),
permitting localization and trapping of low branch (LB) polaritons imposed by
the variation of the waveguide radius in longitudinal direction. We have shown
that critical temperature of BEC occurring in the system can be high enough --
few hundred Kelvins; it is connected with photon-like character of LB
polaritons and strongly depends on waveguide cavity parameters. In the case of
a linear trapping potential we obtain an Airy-shaped polariton condensate wave
function which, when disturbed out of equilibrium, exhibits small amplitude
oscillations with the characteristic period in the picosecond domain.
