  In this paper we study Cauchy problem for thermoelastic plate equations with
friction or structural damping in $\mathbb{R}^n$, $n\geq1$, where the heat
conduction is modeled by Fourier's law. We explain some qualitative properties
of solutions influenced by different damping mechanisms. We show which damping
in the model has a dominant influence on smoothing effect, energy estimates,
$L^p-L^q$ estimates not necessary on the conjugate line, and on diffusion
phenomena. Moreover, we derive asymptotic profiles of solutions in a framework
of weighted $L^1$ data. In particular, sharp decay estimates for lower bound
and upper bound of solutions in the $\dot{H}^s$ norm ($s\geq0$) are shown.
