  The resonant part of the $B_{1g}$ electronic Raman scattering response is
calculated within the $t-J$ model on a planar lattice as a function of
temperature and hole doping, using a finite-temperature diagonalization method
for small systems. Results, directly applicable to experiments on cuprates,
reveal on doping a very pronounced increase of the width of the two-magnon
Raman peak, accompanied by a decrease of the total intensity. At the same time
the peak position does not shift substantially in the underdoped regime.
