An inverse heat conduction problem arises when temperature measurements are taken in the interior of a body, and the temperature and heat flux on the surface are desired. A new approach to the solution of this class of problems is introduced. It relies on the concept of state and disturbance observers which is well-known from systems theory. The complete temperature profile in the heat conducting body as well as the surface heat flux and temperature can be computed from one or several interior temperature measurements by means of a non-linear distributed parameter observer. The technique is introduced and analysed theoretically by means of a simple tutorial example. The approach is finally applied to a difficult inverse problem of technical significance. The time history of local heat flux and temperature oscillations at the inner surface of an evaporator tube are estimated during transition boiling conditions. Experimental results with boiling refrigerant R114 flowing upward in an electrically heated tube are presented.