  The frame-indifferent thermodynamically-consistent model of
thermoviscoelasticity at large strain is formulated in the reference
configuration with using the concept of the second-grade nonsimple materials.
We focus on physically correct viscous stresses that are frame indifferent
under time-dependent rotations. Also elastic stresses are frame indifferent
under rotations and respect positivity of the determinant of the deformation
gradient. The heat transfer is governed by the Fourier law in the actual
deformed configuration, which leads to a nontrivial description when pulled
back into the reference configuration. Existence of weak solutions in the
quasistatic setting, i.e.\ inertial forces are ignored, is shown by time
discretization.
