  It was shown in previous work that when a gravitational wave (GW) passes
through a viscous shell of matter the magnitude of the GW will be damped and
there are astrohysical circumstances in which the damping is almost complete.
The energy transfer from the GWs to the fluid will increase its temperature. We
construct a model for this process and obtain an expression for the temperature
distribution inside the shell in terms of spherical harmonics. Further, it is
shown that this effect is astrophysically significant: a model problem is
constructed for which the temperature increase is of order $10^6{}^\circ$K.
