  We study a generalization of the Pokrovski--Vinogradov model for flows of
solutions and melts of an incompressible viscoelastic polymeric medium to
nonisothermal flows in an infinite plane channel under the influence of
magnetic field. For the linearized problem (when the basic solution is an
analogue of the classical Poiseuille flow for a viscous fluid described by the
Navier-Stokes equations) we find a formal asymptotic representation for the
eigenvalues under the growth of their modulus. We obtain a necessary condition
for the asymptotic stability of a Poiseuille-type shear flow.
