Summary: We consider the inverse problem of determining the spatial dependence \(f(x)\) of the source term in a heat equation \(\partial_tu-\gamma\Delta u=f(x)\sigma(t)\) in \(\Omega\times (0,T)\) assuming \(\sigma(t)\) known, from a single internal measurements of the solution in \(\mathcal O\times (0,T)\). The purpose of this paper is to establish a reconstruction formula for \(f(x)\) similar to the one obtained by M. Yamamoto [Inverse Probl. 11, No. 2, 481–496 (1995; Zbl 0822.35154)], for hyperbolic equations using exact controls, and generalized here for parabolic equations. The reconstruction formula is associated to a family of exact controls \(\nu^{(\tau)}\) indexed by \(\tau\in(0,T)\). We perform numerical simulations in order to illustrate the feasibility, accuracy and stability of the proposed reconstruction formula.