  We investigate a quasilinear system consisting of the Westervelt equation
from nonlinear acoustics and Pennes bioheat equation, subject to Dirichlet or
Neumann boundary conditions. The concept of maximal regularity of type
$L_p$-$L_q$ is applied to prove local and global well-posedness. Moreover, we
show by a parameter trick that the solutions regularize instantaneously.
Finally, we compute the equilibria of the system and investigate the long-time
behaviour of solutions starting close to equilibria.
