  \begin{abstract} We study the Morse-Smale property for the following scalar
semilinear parabolic equation on the circle $S^1$, \begin{equation*}
u_{t}=u_{xx}+f(t,u,u_{x}),\,\,t>0,\,x\in S^{1}=\mathbb{R}/2\pi \mathbb{Z},
\end{equation*} where $f$ is a $C^2$ function and $T$-periodic in $t$. Assume
that the equation admits a compact global attractor $\mathcal{A}$ and let $P$
be the Poincar\'{e} map of this equation. We exclude homoclinic connection for
hyperbolic fixed points of $P$ and prove that stable and unstable manifolds for
any two heteroclinic hyperbolic fixed points of $P$ intersect transversely.
Further, this equation admits the Morse-Smale property provided that all
$\omega$-limit sets (in the case $f(t,u,u_x)=f(t,u,-u_x)$, the $\omega$-limit
set is just a fixed point) of the corresponding Poincar\'{e} map are
hyperbolic. \end{abstract}
