We present subarcsecond imaging in [Ne V] of N49, the brightest optical SNR in the LMC. Between the "cool" optical and "hot" X-ray regimes, [Ne V] emission indicates intermediate temperatures for collisionally excited plasmas (2-6 × 10⁵ K), for which imaging has been extremely limited. We compare the flux in these images to the O VI measured spectroscopically by FUSE in individual apertures and find dereddened line ratios that are reasonably consistent with our predictions for intermediate velocity shocks. The overall luminosity in [Ne V] for the entire remnant is 1.2 × 10³⁶ ergs s^-1, which, given the measured line ratios, implies an overall O VI luminosity of 1.5 × 10³⁸ ergs s^-1. These large radiative losses indicate that this material must have been shocked recently relative to the total lifetime of the remnant. We also explore the complex spatial structure. We find [Ne V] tracing the [O III] emission more closely than it does Hα, measure significant shifts (~0.1 pc) between the peaks of different emission lines, and find 2 orders of magnitude variations in the flux ratios for different filaments across the remnant. These properties, as well as the general filamentary character of the optical emission, suggest thermally unstable intermediate-velocity shocks.