  Current dual-frequency magneto-optical traps for ultracold molecules are
plagued by sub-Doppler heating effects, making them vastly inferior to standard
atomic MOTs. Here we demonstrate theoretically that the sub-Doppler effects in
such a MOT can be engineered to provide cooling instead of heating. We give an
intuitive picture how to achieve such cooling and show the cooling and trapping
force results of the 16 level optical Bloch equations for the case of CaF
molecules. From three-dimensional Monte Carlo simulations we estimate the
temperature and density of our MOT to be $40 \mu K$ and $4 \times 10^8 cm^{-3}$
respectively for a molecule number of $10^5$.
