  We develop a complete theoretical description of photoassociative Stimulated
Raman Adiabatic Passage (STIRAP) near a Feshbach resonance in a thermal atomic
gas. We show that it is possible to use low intensity laser pulses to directly
excite the continuum at a Feshbach resonance and transfer nearly the entire
atomic population to the lowest rovibrational level in the molecular ground
state. In case of a broad resonance, commonly found in several diatomic alkali
molecules, our model predicts a transfer efficiency $\eta$ up to 97% for a
given atom pair, and up to 70% when averaged over an atomic ensemble. The laser
intensities and pulse durations needed for optimal transfer are $10^2-10^3$
W/cm$^2$ and several $\mu$s. Such efficiency compares to or surpasses currently
available techniques for creating stable diatomic molecules, and the
versatility of this approach simplifies its potential use for many molecular
species.
