For certain values of the material parameters, certain viscoelastic fluid models allow for a nonmonotonic relationship between the shear stress and shear rate in simple flows. We consider channel flow of such a fluid, the Johnson-Segalman liquid, subjected to exothermic reactions. A numerical algorithm based on the finite difference method is implemented in time and space for the solution process of the highly nonlinear governing equations. The phenomenon of shear banding is observed and explained in terms of the jump discontinuities in shear rates. We demonstrate that for a reacting Johnson-Segalman fluid, the shear banding can be catastrophic as it leads to large temperature buildup within the fluid and hence makes it easily susceptible, say, to thermal runaway. We also demonstrate that the shear banding can be eliminated by making the walls porous and hence allowing for suction and injection. The suction/injection flow is shown to significantly decrease fluid temperatures for the nonmonotonic viscoelastic Johnson-Segalman model but leads to significant temperature increases for the monotonic viscoelastic Oldroyd-B model.