  According to the Nernst theorem or, equivalently, the third law of
thermodynamics, the absolute zero temperature is not attainable. Starting with
an initial positive temperature, we show that there exist solutions to a
Kelvin-Voigt model for quasi-static nonlinear thermoviscoelasticity at a
finite-strain setting [Mielke-Roub\'i\v{c}ek '20], obeying an
exponential-in-time lower bound on the temperature. Afterwards, we focus on the
case of deformations near the identity and temperatures near a critical
positive temperature, and we show that weak solutions of the nonlinear system
converge in a suitable sense to solutions of a system in linearized
thermoviscoelasticity. Our result extends the recent linearization result in
[Badal-Friedrich-Kru\v{z}\'ik '23], as it allows the critical temperature to be
positive.
