In this paper the linear stability of plane Poiseuille flow is studied for a non-Newtonian liquid having an exponential viscosity-temperature dependence. Non-Newtonian behavior of the fluid is modeled through Carreau rheological equation. Channel walls are kept at constant but different temperatures. Steady base flow equations and equations describing the evolution of small, two-dimensional disturbances are derived and solved numerically. The stability problem is formulated as an eigenvalue problem for a set of ordinary differential equations. Discritization is performed using a pseudospectral technique based on Chebyshev polynomials expansions. The resulting generalized matrix eigenvalue problem is solved using the QZ algorithm. The results presenting the influence of temperature and shear-rate dependent viscosity on the stability are given in the form of marginal stability curves for a wide range of flow and fluid dimensionless parameters, including channel wall temperature difference ΔT̄, material time constant λ, and power-law index n.