  Standard cavity cooling of atoms or dielectric particles is based on the
action of dispersive optical forces in high-finesse cavities. We investigate
here a complementary regime characterized by large cavity losses, resembling
the standard Doppler cooling technique. For a single two-level emitter a
modification of the cooling rate is obtained from the Purcell enhancement of
spontaneous emission in the large cooperativity limit. This mechanism is aimed
at cooling of quantum emitters without closed transitions, which is the case
for molecular systems, where the Purcell effect can mitigate the loss of
population from the cooling cycle. We extend our analytical formulation to the
many particle case governed by weak individual coupling but exhibiting
collective strong Purcell enhancement to a cavity mode.
