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In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if $(t,x)\in R_{+}\times \Omega$ u = 0 if $(t,x)\in R_{+}\times \partial \Omega$, where $\Omega \subset R^N$ is a bounded domain with smooth boundary ∂Ω and $g:R_{+}\times \overline{\Omega }\times R\to R$ is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.