  We derive a von K\'arm\'an plate theory from a three-dimensional quasistatic
nonlinear model for nonsimple thermoviscoelastic materials in the Kelvin-Voigt
rheology, in which the elastic and the viscous stress tensor comply with a
frame indifference principle [Mielke-Roub\'{i}\v{c}ek '20]. In a
dimension-reduction limit, we show that weak solutions to the nonlinear system
of equations converge to weak solutions of an effective two-dimensional system
featuring mechanical equations for viscoelastic von K\'arm\'an plates,
previously derived in [Friedrich-Kru\v{z}\'ik '20], coupled with a linear
heat-transfer equation. The main challenge lies in deriving a priori estimates
for rescaled displacement fields and temperatures, which requires the
adaptation of generalized Korn's inequalities and bounds for heat equations
with $L^1$-data to thin domains.
