We present millimeter (80-230 GHz), radio (6-45 GHz), and X-ray (0.2-10 keV) observations of ZTF20acigmel (AT2020xnd), a short-duration luminous optical transient at z = 0.2433. The 100 GHz peak luminosity is similar to that of long-duration gamma-ray bursts (2 × 10 30 erg s −1 Hz −1 ) but the light curve rises on a much longer timescale (one month). In the standard framework of synchrotron self-absorption of electrons in a power-law energy distribution, the data imply a fast (v ≈ 0.2c) shock with large energy (U 10 49 erg) propagating in a medium with a steep (n e ∝ r −3 ) density profile. The forward-shock properties are similar to those of the fast-luminous transient AT2018cow, and in both cases the model for the late-time (∆t > 70 d) low-frequency (ν < 40 GHz) data is not consistent with the early-time (∆t < 40 d) high-frequency (ν > 70 GHz) emission. Motivated by the observation of a steep spectral index (f ν ∝ ν −2 ) across the millimeter bands, we favor a thermal electron population (relativistic Maxwellian) for the synchrotron emission, the first such inference for a cosmic explosion. We find that the X-ray luminosity of L X ≈ 10 43 erg s −1 exceeds simple predictions from the radio and UVOIR luminosity and likely has a separate physical origin, such as a central engine. Our work suggests that luminous millimeter, radio, and X-ray emission are a generic feature of transients with fast (≈ 3 d) and luminous (M ≈ −21 mag) optical light curves. We estimate the rate at which transients like AT2018cow and AT2020xnd will be detected by future wide-field millimeter transient surveys like CMB-S4, and conclude that energetic explosions in dense environments may represent a significant population of extragalactic transients in the 100 GHz sky.