We examine the inverse problem of locating and describing an
internal point defect in a one-dimensional rod $\Omega$ by
controlling the heat inputs and measuring the subsequent
temperatures at the boundary of $\Omega$. We use a variation of
the forward heat equation to model heat flow through $\Omega$,
then propose algorithms for locating an internal defect and
quantifying the effect the defect has on the heat flow. We
implement these algorithms, analyze the stability of the
procedures, and provide several computational examples.