The nuclei of merging galaxies are often deeply buried in dense layers of gas and dust . In these regions , gas outflows driven by starburst and active galactic nuclear activity are believed to play a crucial role in the evolution of these galaxies . However , to fully understand this process it is essential to resolve the morphology and kinematics of such outflows . Using near-infrared integral-field spectroscopy obtained with SINFONI on the Very Large Telescope , we detect a kpc-scale structure of high-velocity molecular hydrogen ( H _ { 2 } ) gas associated with the deeply buried secondary nucleus of the infrared-luminous merger-galaxy NGC 3256 . We show that this structure is most likely the hot component of a molecular outflow , which is detected also in the cold molecular gas by Sakamoto et al . This outflow , with a total molecular gas mass of M _ { H _ { 2 } } \sim 2 \times 10 ^ { 7 } M _ { \odot } , is among the first to be spatially resolved in both the hot molecular H _ { 2 } gas with VLT/SINFONI and the cold molecular CO emitting gas with ALMA . The hot and cold components share a similar morphology and kinematics , with a hot-to-cold molecular gas mass ratio of \sim 6 \times 10 ^ { -5 } . The high ( \sim 100 pc ) resolution at which we map the geometry and velocity structure of the hot outflow reveals a biconical morphology with opening angle \sim 40 ^ { \circ } and gas spread across a FWZI \sim 1200 km s ^ { -1 } . Because this collimated outflow is oriented close to the plane of the sky , the molecular gas may reach maximum intrinsic outflow velocities of \sim 1800 km s ^ { -1 } , with an average mass outflow rate of at least Ṁ _ { outfl } \sim 20 M _ { \odot } yr ^ { -1 } . By modeling the line-ratios of various near-infrared H _ { 2 } transitions , we show that the H _ { 2 } -emitting gas in the outflow is heated through shocks or X-rays to a temperature of T \sim 1900 \pm 300 K. The energy needed to drive the collimated outflow is most likely provided by a hidden Compton-thick AGN or by the nuclear starburst . We show that the global kinematics of the molecular outflow that we detect in NGC 3256 mimic those of CO-outflows that have been observed at much lower spatial resolution in starburst- and active galaxies .