  Complex turbulent motions of magnetized gas are ubiquitous in the
interstellar medium. The source of this turbulence, however, is still poorly
understood. Previous work suggests that compression caused by supernova
shockwaves, gravity, or cloud collisions, may drive the turbulence to some
extent. In this work, we present three-dimensional (3D) magnetohydrodynamic
(MHD) simulations of contraction in turbulent, magnetized clouds from the warm
neutral medium (WNM) of the ISM to the formation of cold dense molecular
clouds, including radiative heating and cooling. We study different contraction
rates and find that observed molecular cloud properties, such as the
temperature, density, Mach number, and magnetic field strength, and their
respective scaling relations, are best reproduced when the contraction rate
equals the turbulent turnover rate. In contrast, if the contraction rate is
significantly larger (smaller) than the turnover rate, the compression drives
too much (too little) turbulence, producing unrealistic cloud properties. We
find that the density probability distribution function evolves from a double
log-normal representing the two-phase ISM, to a skewed, single log-normal in
the dense, cold phase. For purely hydrodynamical simulations, we find that the
effective driving parameter of contracting cloud turbulence is natural to
mildly compressive (\mbox{$b\sim0.4$--$0.5$}), while for MHD turbulence, we
find \mbox{$b\sim0.3$--$0.4$}, i.e., solenoidal to naturally mixed. Overall,
the physical properties of the simulated clouds that contract at a rate equal
to the turbulent turnover rate, indicate that large-scale contraction may
explain the origin and evolution of turbulence in the ISM.
