An adiabatic uniaxial elastic tension in non-oriented polymers (polyethylene, polypropylene) has been found to cause a cooling that is sharper than linear (with respect to stress sigma), and close to the quadratic dependence on sigma. In this paper we suggest a thermodynamic derivation of the Delta T(sigma) dependence (where Delta T is the change in temperature of an elastic body on loading) that takes into account the temperature dependence of the elastic modulus. A more general expression for Delta T(sigma) (compared to the Kelvin expression) derived here, gives a satisfactory explanation of the observed non-linearity of Delta T(sigma) just for polymers.