  In this paper, we develop a factorization method to reconstruct cavities in a
heat conductor by knowing the Neumann-to-Dirichlet map at the boundary of this
conductor. The factorization method is a very well known reconstruction method
for inverse problems described by self-adjoint elliptic equations. It enables
us to reconstruct the boundaries of unknown targets such as cavities and
inclusions. This method was successfully applied for examples to the inverse
scattering problem by obstacles for the acoustic wave and the electrical
impedance tomography problem. The forward model equations for these problems
are the Helmholtz equation and the conductivity equation which are both
self-adjoint equations. On the other hand, the heat equation is a typical
non-selfadjoint equation. This paper is giving the first attempt to study the
factorization method for inverse problems whose forward model equations are
non-selfadjoint. We emphasize that an auxiliary operator introduced in this
paper is the key which makes this attempt successful. This operator connects
the back projection operators for the forward and backward heat equations.
