  In many black hole systems, the accretion disk is expected to be misaligned
with respect to the black hole spin axis. If the scale height of the disk is
much smaller than the misalignment angle, the spin of the black hole can tear
the disk into multiple, independently precessing `sub-disks'. This is most
likely to happen during outbursts in black hole X-Ray binaries (BHXRBs) and in
active galactic nuclei (AGN) accreting above a few percent of the Eddington
limit, because the disk becomes razor-thin. Disk tearing has the potential to
explain variability phenomena including quasi-periodic oscillations (QPOs) in
BHXRBs and changing-look phenomena in AGN. Here, we present the first radiative
two-temperature GRMHD simulation of a strongly tilted ($65^{\circ}$) accretion
disk around a $M_{BH}=10M_{\odot}$ black hole, which tears and precesses. This
leads to luminosity swings between a few percent and $50 \%$ of the Eddington
limit on sub-viscous timescales. Surprisingly, even where the disk is radiation
pressure dominated, the accretion disk is thermally stable over $t \gtrsim
21,000 r_g/c$. This suggests warps play an important role in stabilizing the
disk against thermal collapse. The disk forms two nozzle shocks perpendicular
to the line of nodes where the scale height of the disk decreases $10$-fold and
the electron temperature reaches $T_e \sim 10^8-10^9 K$. In addition, optically
thin gas crossing the tear between the inner and outer disk gets heated to $T_e
\sim 10^8 K$. This suggests that warped disks may emit a Comptonized spectrum
that deviates substantially from idealized models.
