We consider a system coupling the Westervelt equation with a hyperbolic version of the Pennes bioheat
equation. This model describes the heating generated by the propagation of nonlinear ultrasonic waves
through thermo-viscous media, which has many industrial and medical applications. More precisely, the
equations are coupled through the dependence of the coeffcients in the Westervelt equation on the tem-
perature and through a source term in the Pennes equation accounting for the absorbed acoustic energy. \\
Using energy methods together with a continuity argument, we prove the global well-posedness of
the system under consideration. To this end, we establish time-independent energy estimates that ensure
uniform boundedness of the solution for all times. In addition, by relying on Sobolev embeddings and
interpolation inequalities, global well-posedness is achieved under a smallness assumption imposed only
on suitable lower-order norms of the initial data. Furthermore, by combining the derived estimates with
a Gronwall-type inequality, we show the exponential decay of the solution to the steady state.