  Recently it has been found that, when operated at large input power, the
linewidth of terahertz radiation emitted from intrinsic Josephson junction
stacks can be as narrow as some megahertz. In this high-bias regime a hot spot
coexists with regions which are still superconducting. Surprisingly, the
linewidth was found to decrease with increasing bath temperature. We present a
simple model describing the dynamics of the stack in the presence of a hot spot
by two parallel arrays of pointlike Josephson junctions and an additional shunt
resistor in parallel. Heat diffusion is taken into account by thermally
coupling all elements to a bath at temperature T_b. We present current-voltage
characteristics of the coupled system and calculations of the linewidth of the
radiation as a function of T_b. In the presence of a spatial gradient of the
junction parameters critical current and resistance, the linewidth deceases
with increasing T_b, similar to the experimental observation.
