In this paper we prove a symmetry theorem for the Green function associated to the heat equation in a certain class of bounded domains \Omega\subset\mathbb{R}^{n+1} . For T>0 , let \Omega_T=\Omega\cap[\mathbb{R}^n\times (0,T)] and let G be the Green function of \Omega_T with pole at (0,0)\in\partial_p\Omega_T . Assume that the adjoint caloric measure in \Omega_T defined with respect to (0,0) , \hat\omega , is absolutely continuous with respect to a certain surface measure, \sigma , on \partial_p\Omega_T . Our main result states that if \frac {d\hat\omega}{d\sigma}(X,t)=\lambda\frac {|X|}{2t} for all (X,t)\in \partial_p\Omega_T\setminus\{(X,t): t=0\} and for some \lambda>0 , then \partial_p\Omega_T\subseteq\{(X,t):W(X,t)=\lambda\} where W(X,t) is the heat kernel and G=W-\lambda in \Omega_T . This result has previously been proven by Lewis and Vogel under stronger assumptions on \Omega .