Non-conventional heating treatments, such as Joule heating, can produc
e materials with attractive physical properties. Although extensively
explored in amorphous wires and ribbons, one of the major drawbacks of
the technique is the intrinsic difficulty in determining the annealin
g temperature. The temperature behaviour of two selected wires submitt
ed to a DC electrical current of increasing amplitude was calibrated b
y comparing the temperature dependence of the material's saturation ma
gnetization obtained during Joule heating to that measured during conv
entional annealing in a furnace. As a result, a correlation between th
e average temperature and current density was obtained. A theory descr
ibing the thermal effects of a continuous current flow in amorphous wi
res is proposed, showing that the thermal treatment is nearly uniform
over the entire wire volume, under typical experimental conditions. Th
e effect of fluctuations of the wire diameter on the steady-state temp
erature is also discussed.