Turbulent drag reduction efficiencies (%DR) of aqueous poly (ethylene oxide) solutions at various distances tau = (T-theta-T)/T-theta away from the theta temperature (T-theta) are studied. It is found that only the long-time behavior of %DR of the system is sensitive to tau in that %DR decays faster for systems closer to the theta-point. Usually, this faster decay is attributed to the faster mechanical molecular degradation (MMD) of polymers in bad solvents produced by turbulence. However, temperature quenches experiments close to T-theta show that the apparent faster decrease in %DR for polymers closer to T-theta is not due to MMD but rather because of the shrinking of the polymer after they have been injected into the turbulent flow. The relative insensitivity of the initial maximum %DR can be understood if T-theta is considered as a function of the flow.