  Observations of the extragalactic ($z=0.0141$) transient AT2018cow
established a new class of energetic explosions shocking a dense medium, which
produce luminous emission at millimeter and sub-millimeter wavelengths. Here we
present detailed millimeter- through centimeter-wave observations of a similar
transient, ZTF20acigmel (AT2020xnd) at $z=0.2433$. Using observations from the
NOrthern Extended Millimeter Array and the Very Large Array, we model the
unusual millimeter and radio emission from AT2020xnd under several different
assumptions, and ultimately favor synchrotron radiation from a thermal electron
population (relativistic Maxwellian). The thermal-electron model implies a fast
but sub-relativistic ($v\approx0.3c$) shock and a high ambient density
($n_e\approx4\times10^{3}$cm$^{-3}$ at $\Delta t\approx40$ days). The X-ray
luminosity of $L_X\approx10^{43}$ erg sec$^{-1}$ exceeds simple predictions
from the radio and UVOIR luminosity and likely has a separate physical origin,
such as a central engine. Using the fact that month-long luminous
($L_\nu\approx 2\times10^{30}$ erg sec$^{-1}$ Hz$^{-1}$ at 100 GHz) millimeter
emission appears to be a generic feature of transients with fast
($t_{1/2}\approx3$ days) and luminous ($M_\mathrm{peak}\approx -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 such as CMB-S4, and conclude that energetic explosions in dense
environments may represent a significant population of extragalactic transients
in the 100 GHz sky.
