  In this paper, we model the observable signatures of tidal disruptions of
white dwarf (WD) stars by massive black holes (MBHs) of moderate mass, $\approx
10^3 - 10^5 M_\odot$. When the WD passes deep enough within the MBH's tidal
field, these signatures include thermonuclear transients from burning during
maximum compression. We combine a hydrodynamic simulation that includes nuclear
burning of the disruption of a $0.6 M_\odot$ C/O WD with a Monte Carlo
radiative transfer calculation to synthesize the properties of a representative
transient. The transient's emission emerges in the optical, with lightcurves
and spectra reminiscent of type I SNe. The properties are strongly
viewing-angle dependent, and key spectral signatures are $\approx 10,000$ km
s$^{-1}$ Doppler shifts due to the orbital motion of the unbound ejecta.
Disruptions of He WDs likely produce large quantities of intermediate-mass
elements, offering a possible production mechanism for Ca-rich transients.
Accompanying multiwavelength transients are fueled by accretion and arise from
the nascent accretion disk and relativistic jet. If MBHs of moderate mass exist
with number densities similar to those of supermassive MBHs, both high energy
wide-field monitors and upcoming optical surveys should detect tens to hundreds
of WD tidal disruptions per year. The current best strategy for their detection
may therefore be deep optical follow up of high-energy transients of
unusually-long duration. The detection rate or the non-detection of these
transients by current and upcoming surveys can thus be used to place meaningful
constraints on the extrapolation of the MBH mass function to moderate masses.
