Linear stability analysis of Taylor-Couette flow of dilute polymeric solutions has been performed by using two prototypical constitutive equations for polymeric solutions, namely, the Oldroyd-B and the FENE-P models. The hydrodynamic stability characteristics of the flow in the presence and absence of thermal effects and in the limit of vanishing fluid inertia have been determined using an eigenvalue analysis. Particular attention has been paid to accurately determine the instability onset conditions as a function of fluid thermal sensitivity and gap ratio. We observed a reduction in the critical Weissenberg, Wi(c), for the instability onset as the gap ratio and fluid thermal sensitivity are enhanced. In particular, under non-isothermal conditions, Wi(c) was reduced by almost an order of magnitude for all gap ratios. Our results suggest that recent experiments leading to observations of "purely elastic turbulence" in the Taylor-Couette flow at order (1) Wi by Groisman and Steinberg (2004) [1] were not performed under isothermal conditions. Hence, this new flow state should be labeled "thermo-elastic turbulence." (C) 2014 Elsevier B.V. All rights reserved.