We present JWST broadband images of the highly inclined protoplanetary disk SSTc2d J163131.2-242627 (Oph163131) from 2.0 to 21 μm. The images show a remarkable evolution in disk structure with wavelength, quite different from previous JWST observations of other edge-on disks. At 2.0 and 4.4 μm, Oph163131 shows two scattering surfaces separated by a dark lane, typical of highly inclined disks. Starting at 7.7 μm, however, (1) the two linear nebulosities flanking the dark lane disappear; (2) the brighter nebula tracing the disk upper surface transitions into a compact central source distinctly larger than the JWST point-spread function and whose intrinsic size increases with wavelength; and (3) patches of extended emission appear at low latitudes, and at surprisingly large radii nearly twice that of the scattered light seen with Hubble Space Telescope and NIRCam, and of the gas. We interpret the compact central source as thermal emission from the star and the inner disk that is not seen directly, but which instead is able to progressively propagate to greater distances at longer wavelengths. The lack of sharp-edged structures in the extended patchy emission argues against the presence of shocks and suggests photoexcitation or stochastic heating of material smoothly flowing away from the star along the disk surface. Finally, the dark lane thickness decreases significantly between 0.6 and 4.4 μm, which indicates that the surface layers of Oph163131 lack grains larger than 1 μm.