We present a new 400-ks Chandra X-ray observation of the merging galaxy cluster Abell 2146. This deep observation reveals detailed structure associated with the major merger event including the Mach number M= 2.3 ± 0.2 bow shock ahead of the dense, ram pressure stripped subcluster core and the first known example of an upstream shock in the intracluster medium (ICM) (M= 1.6 ± 0.1). By measuring the electron temperature profile behind each shock front, we determine the time-scale for the electron population to thermally equilibrate with the shock-heated ions. We find that the temperature profile behind the bow shock is consistent with the time-scale for Coulomb collisional equilibration and the post-shock temperature is lower than expected for instant shock heating of the electrons. Although like the Bullet cluster the electron temperatures behind the upstream shock front are hotter than expected, favouring the instant heating model, the uncertainty on the temperature values is greater here and there is significant substructure complicating the interpretation. We also measured the width of each shock front and the contact discontinuity on the leading edge of the subcluster core to investigate the suppression of transport processes in the ICM. The upstream shock is ∼440 kpc in length but appears remarkably narrow over this distance with a best-fitting width of only 6+5−3 kpc compared with the mean free path of 23 ± 5 kpc. The leading edge of the subcluster core is also narrow with an upper limit on the width of only 2 kpc separating the cool, multiphase gas at 0.5–2 keV from the shock-heated surrounding ICM at ∼6 keV. The strong suppression of diffusion and conduction across this edge suggests a magnetic draping layer may have formed around the subcluster core. The deep Chandra observation has also revealed a cool, dense plume of material extending ∼170 kpc perpendicular to the merger axis, which is likely to be the disrupted remnant of the primary cluster core. This asymmetry in the cluster morphology indicates the merger has a non-zero impact parameter. We suggest that this also explains why the south-western edge of the subcluster core is narrow and stable over ∼150 kpc in length, but the north-eastern edge is broad and being stripped of material.