  The heat equation does not have time-reversal invariance. However, using a
solution of an associated wave equation which has time-reversal invariance, one
can establish an explicit extraction formula of the minimum sphere that is
centered at an arbitrary given point and encloses an unknown cavity inside a
heat conductive body. The data employed in the formula consist of a special
heat flux depending on a large parameter prescribed on the surface of the body
over an arbitrary fixed finite time interval and the corresponding temperature
field. The heat flux never blows up as the parameter tends to infinity. This is
different from a previous formula for the heat equation which also yields the
minimum sphere. In this sense, the prescribed heat flux is moderate.
