  We analyze cavity-assisted cooling schemes for polar molecules in the
microwave domain, where molecules are excited on a rotational transition and
energy is dissipated via strong interactions with a lossy stripline cavity, as
recently proposed by A. Andre et al., Nature Physics 2, 636 (2006). We identify
the dominant cooling and heating mechanisms in this setup and study cooling
rates and final temperatures in various parameter regimes. In particular we
analyze the effects of a finite environment temperature on the cooling
efficiency, and find minimal temperature and optimized cooling rate in the
strong drive regime. Further we discuss the trade-off between efficiency of
cavity cooling and robustness with respect to ubiquitous imperfections in a
realistic experimental setup, such as anharmonicity of the trapping potential.
