  We use thermal noise induced currents to image the real and imaginary parts
of the conductivity of a body. Covariances of the thermal noise currents
measured at a few electrodes are shown to be related to a deterministic
problem. We use the covariances obtained while selectively heating the body to
recover the real power density in the body under known boundary conditions and
at a known frequency. The resulting inverse problem is related to
acousto-electric tomography, but where the conductivity is complex and only the
real power is measured. We study the local solvability of this problem by
determining where its linearization is elliptic. Numerical experiments
illustrating this inverse problem are included.
