We introduce a variation of the dissipative particle dynamics (DPD) thermostat that allows for controlling transport properties of molecular fluids. The standard DPD thermostat acts only on a relative velocity along the interatomic axis. Our extension includes the damping of the perpendicular components of the relative velocity, whilst keeping the advantages of conserving Galilei invariance and within our error bar also hydrodynamics. This leads to a second friction parameter for tuning the transport properties of the system. Numerical simulations of a simple Lennard-Jones fluid and liquid water demonstrate a very sensitive behaviour of the transport properties, e.g., viscosity, on the strength of the new friction parameter. We envisage that the new thermostat will be very useful for the coarse-grained and adaptive resolution simulations of soft matter, where the diffusion constants and viscosities of the coarse-grained models are typically too high/low, respectively, compared to all-atom simulations.