  We consider the linear thermoelastic plate equations with free boundary
conditions in uniform $C^4$-domains, which includes the half-space, bounded and
exterior domains. We show that the corresponding operator generates an analytic
semigroup in $L^p$-spaces for all $p\in(1,\infty)$ and has maximal
$L^q$-$L^p$-regularity on finite time intervals. On bounded $C^4$-domains, we
obtain exponential stability.
