  We present a comprehensive study of the temperature and doping dependence of
the 500 meV peak observed at ${\bf q}=(\pi,0)$ in resonant inelastic x-ray
scattering (RIXS) experiments on $\rm La_2CuO_4$. The intensity of this peak
persists above the N\'eel temperature (T$_{N}$=320 K), but decreases gradually
with increasing temperature, reaching zero at around T=500 K. The peak energy
decreases with temperature in close quantitative accord with the behavior of
the two-magnon $\rm B_{1g}$ Raman peak in $\rm La_2CuO_4$, and with suitable
rescaling, agrees with the Raman peak shifts in $\rm EuBa_2Cu_3O_6$ and $\rm
K_2NiF_4$. The overall dispersion of this excitation in the Brillouin zone is
found to be in agreement with theoretical calculations for a two-magnon
excitation. Upon doping, the peak intensity decreases analogous to the Raman
mode intensity and appears to track the doping dependence of the spin
correlation length. Taken together, these observations strongly suggest that
the 500 meV mode is magnetic in character and is likely a two-magnon
excitation.
