Molecular hydrogen (H2) is the most important tracer of velocity shocks in the bow shocks of well-collimated Herbig-Haro (HH) jets and also in less well-collimated molecular outflows. Yet not much is known about which type of molecular physics is appropriate for these objects and which flow pattern (e.g., J shocks or C shocks) excites the H2. Only two outflows have been studied in detail so far, with differing results. What is clearly necessary to understand the shock structures that arise in the shock waves of bipolar outflows is the knowledge of the excitation state of the gas as measured by the column density of H2 in each energy level in a number of typical objects. However, only lines arising from energy levels higher than about 6000 K are accessible from the ground. We therefore propose to derive spatially resolved level column densities from the purely rotational transitions of the H2 molecule from energy levels of only 1680 - 4600 K through ISOCAM images. The excitation of these lines is expected to be purely collisional, meaning that the conditions in the emitting gas can be deduced conclusively, and an unequivocal decision between J shock models and C shock models is feasible. Continuum emission from hot dust (T about 1000 K) may, however, contribute significantly to the measured fluxes. Hardly anything is known about the occurrence and distribution of hot dust in outflows, yet the dust grains may play an important role in the reformation of molecules behind the shock fronts. So while we need to observe the emission from hot dust to discriminate between the line emission from H2 and the dust continuum, this offers the superb chance to study the occurrence and distribution of hot dust in the bipolar outflows from YSOs at no extra cost.